Keywords: Stability of nonlinear systems, Numerical algorithms, Lyapunov methods
Abstract: A dynamical system is mixed monotone if its vector field or update-map is decomposable into an increasing component and a decreasing component. In this tutorial paper, we study both continuous-time and discrete-time mixed monotonicity and consider systems subject to an input that accommodates, emph{e.g.}, unknown parameters, an unknown disturbance input, or an exogenous control input. We first define mixed monotonicity with respect to a decomposition function, and we recall sufficient conditions for mixed monotonicity based on sign properties of the state and input Jacobian matrices for the system dynamics. The decomposition function allows for constructing an embedding system that lifts the dynamics to another dynamical system with twice as many states but where the dynamics are monotone with respect to a particular southeast order. This enables applying the powerful theory of monotone systems to the embedding system in order to conclude properties of the original system. In particular, a single trajectory of the embedding system provides hyperrectangular over-approximations of reachable sets for the original dynamics. In this way, mixed monotonicity enables efficient reachable set approximation for applications such as optimization-based control and abstraction-based formal methods in control systems.

Keywords: Computational methods, Optimization, Stability of nonlinear systems
Abstract: This talk will discuss how one can establish mixed-monotonicity and obtain a decomposition function for a sampled-data system, using only the underlying continuous-time model. Since the solution map and its Jacobian are not in general available analytically we obtain samples of the Jacobian using numerical evaluation of sensitivity matrices, which are the partial derivatives representing the variations of the continuous-time system trajectories in response to variations of the initial states. Using interval arithmetics, we first over-approximate the possible values of the second-order sensitivity. Then we exploit these bounds and the evaluation of the first-order sensitivity matrices at a few sampled initial states to obtain an over-approximation of the first-order sensitivity, which is in turn used to over-approximate the reachable set of the initial system. This approach provides guaranteed over-approximations of the first-order sensitivity, that is the Jacobian of the unknown solution map. Moreover the amount of conservativeness in the over-approximation can be arbitrarily reduced by increasing the number of samples.

Keywords: Computational methods, Optimization, Stability of nonlinear systems
Abstract: In this talk we discuss how the reachability tools presented in the first two talks enable a finite-state abstraction of a continuous-state dynamical model. Finite abstraction is a key prerequisite for most applications of formal methods to control systems. To ensure scalability of the entire abstraction process we exploit sparsity properties of the continuous-state dynamical model and minimize the number of reachability computations by traversing the state space judiciously. Indeed the reachability computations proposed in the first two talks decompose naturally into separate state dimensions, since we determine an interval in each dimension from a single entry of the monotone decomposition function. We can thus leverage the sparsity in the state update equation for significant savings in reachability computations. In addition we store the state transitions by using binary decision diagrams, an efficient data structure for this purpose. When combined, the tools presented in this talk enable us to significantly reduce the runtime and memory requirements of the finite abstraction process.

Keywords: Computational methods, Optimization, Stability of nonlinear systems
Abstract: In this talk, we show how mixed monotonicity is leveraged for formally verifying and synthesizing discrete-time stochastic systems via finite state abstracitons. Finite-state abstractions of stochastic dynamical systems require the use of Interval-valued Markov Chains (IMCs), an extension of Markov chains allowing for the probabilities of transition between states to lie within an interval. We first present an efficient procedure for computing finite-state IMC abstractions of discrete-time, mixed-monotone stochastic systems subject to affine disturbances given a rectangular partition of the state-space. Next, we show how this abstraction is used to formally verify the original system against a linear temporal logic specification by solving a discrete reachability problem on the IMC abstraction. We then show how these results can be further leveraged for synthesizing controllers for systems subject to inputs.

Keywords: Computational methods, Optimization, Stability of nonlinear systems
Abstract: In this talk, we provide an efficient control synthesis algorithm for monotone transition systems and directed safety specifications. Two classes of monotone transition systems are presented: state monotone transition systems and input-state monotone transition systems. For the first class of systems, a partial order is defined only on the state space, for the second, the input space is ordered as well. The introduced lazy synthesis approach is based on the efficient computation of predecessors. It benefits not only from a monotone property of transition systems but also from the ordered structure of the state (input) space and the fact, that directed safety specifications are considered. To enrich the class of the considered specifications, we also present an incremental controller synthesis framework, which allows us to deal with intersections of upper and lower-closed safety requirements. We then compare the proposed approach with the classical safety synthesis algorithm and illustrate the advantages, in terms of run-time and memory efficiency, on an adaptive cruise control problem.

Keywords: Systems biology, Computational methods, Biomedical
Abstract: Live-cell imaging is an important technique to study cell migration and proliferation as well as image-based profiling of drug perturbations over time. To gain biological insights from live-cell imaging data, it is necessary to identify individual cells, follow them over time and extract quantitative information. However, since often biological experiment does not allow the high temporal resolution to reduce excessive levels of illumination or minimize unnecessary oversampling to monitor long-term dynamics, it is still a challenging task to obtain good tracking results with coarsely sampled imaging data. To address this problem, we consider cell tracking problem as ``stable matching problem" and propose a robust tracking method based on Voronoi partition which adapts parameters that need to be set according to the spatio-temporal characteristics of live cell imaging data such as cell population and migration. We demonstrate the performance improvement provided by the proposed method using numerical simulations and compare its performance with proximity-based tracking and nearest neighbor-based tracking.

Keywords: Systems biology, Identification, Machine learning
Abstract: Deep learning systems have emerged as powerful mechanisms for learning domain translation models. However, in many cases, complete information in one domain is assumed to be necessary for sufficient cross-domain prediction. In this work, we motivate a formal justification for domain-specific information separation in a simple linear case and illustrate that a self-supervised approach enables domain translation between data domains while filtering out domain-specific data features. We introduce a novel approach to identify domain-specific information from sets of unpaired measurements in complementary data domains by considering a deep learning cross-domain autoencoder architecture designed to learn shared latent representations of data while enabling domain translation. We introduce an orthogonal gate block designed to enforce orthogonality of input feature sets by explicitly removing non-sharable information specific to each domain and illustrate separability of domain-specific information on a toy dataset.

Keywords: Systems biology, Modeling, Control applications
Abstract: The oscillator made of a negative loop of two genes is one of the most classical motifs of genetic networks. We give solutions to control such an oscillator by modifying the synthesis rates. Our models are given by piecewise affine systems, and the control is qualitative, taking only two values. Thus, the necessary measurements for implementing this control only depend on the fact that some gene is expressed or not. Our first goal is to obtain sustained oscillations. Then we study the control by a sliding mode for negative ODE loops in general, to suppress sustained or damped oscillations. Finally, we introduced a general idea for creating sustained oscillations in systems with damped oscillations following a particular cycle of domains.

Keywords: Biomolecular systems, Biological systems, Systems biology
Abstract: Many biological systems need to sense and respond to chemical gradients in order to find nutrients and adapt to their environment. In nature, molecular networks able to compute molecular gradients are complex, making it challenging to build minimal components for use in synthetic biology. In this work, we propose a motif that relies on molecular sequestration and delays to perform an approximate derivative operation. We analyze and discuss the properties and physical limitations of this network. We outline potential biological implementations of the motif, and we demonstrate with simulations that it can be used as a closed-loop controller for gradient tracking. Other molecular architectures with the topology of an incoherent feedforward loop could be used for derivative computation, but they present nonlinear behavior that is avoided in our motif.

Keywords: Biomolecular systems, Cellular dynamics, Stability of nonlinear systems
Abstract: The limited availability of shared cellular resources introduces strong coupling among seemingly unrelated components. Given the fundamental role that multistable switches play in both natural and synthetic genetic systems, here we focus on how the scarcity of resources affects the behavior of these elementary building blocks. In particular, we reveal that while competition for scarce resources pushes the dynamics towards monostability, self-activation attenuates this phenomenon, as well as perturbations from the genetic context of the switch. However, this robustness comes at a price: our analysis uncovers that strong self-activation can lead to tristable dynamics that can surprisingly and misleadingly appear as if the underlying system was monostable, especially when considering cell-to-cell heterogeneity. This paper thus exposes how self-activation and competition for scarce resources establish stability and robustness properties of genetic switches at both single cell and population levels. Due to their analytic nature, our results provide explicit guidelines for the rational and optimal design of synthetic gene circuits and facilitate the analysis of organizing principles underlying natural systems.

Keywords: Biomolecular systems, Optimization
Abstract: We consider chemical reaction systems that operate in a resource limited situation such as in a closed test tube. These systems can operate only for a finite interval of time before the system variables deviate from the normal operating region. Thus, in order to characterize the performance of the systems, it is important to analyze the duration of the normal operation, which is closely related to the notion of finite-time stability. In this paper, we propose an algebraic optimization approach to analyze finite-time stability of resource limited chemical reactions. Specifically, we present semidefinite programs that compute guaranteed lower and upper bounds of the duration of the normal operation, which we call survival time, for a given set of uncertain initial concentrations. The proposed semidefinite programs provide progressively tighter bounds of survival time by increasing the variables and constraints, allowing for the tuning of the balance between the computational time and the conservativeness of the bounds. We demonstrate the proposed method using the regenerator circuit of DNA strand displacement reactions.

Keywords: Chaotic systems, Identification, Computational methods
Abstract: Oscillatory models of cytosolic calcium concentration are analyzed when two parameters of the models vary simultaneously, yielding two-parameter bifurcation diagrams. The diagrams are obtained through the 0-1 test for chaos and have a resolution of 256 gray levels. The calcium oscillation models have interesting types of steady-state responses, from constant, through periodic oscillations (spiking, bursting and mixed-mode), to chaotic ones. The periodic oscillations have frequencies that change significantly when parameters vary, making the 0-1 test implementation particularly difficult, as an extreme care should be exercised when selecting the length of the solution interval and additional two parameters in the 0-1 test. To create a two-parameter bifurcation diagram one has to solve the underlying model about a million times to identify all the details of the diagram. Such computations are not possible to be done on a single processor computer. Thus, a parallel computing is used in this paper.

Keywords: Stability of nonlinear systems, Metabolic systems, Network analysis and control
Abstract: Motivated by biochemical reaction networks, a generalization of the classical secant condition for the stability analysis of cyclic interconnected fractional-order systems is provided. The main result presents a necessary and sufficient condition for stability of networks of cyclic interconnection of fractional-order systems when the digraph describing the network conforms to a single circuit. Finally, the theoretical results are confirmed via some numerical illustrations.

Keywords: Linear parameter-varying systems, Time-varying systems, LMIs
Abstract: This paper introduces the notion of linear time-varying (LTV) negative imaginary systems. LTV negative imaginary systems are defined using a time-domain dissipative supply rate w(u,dot{y}) that depends on input to the system (u), time-derivative of the system's output (dot{y}) and an index delta geq 0. For delta > 0, it gives rise to a strict subclass within the LTV negative imaginary systems, termed as LTV output strictly negative imaginary systems. For characterizing the proposed class of systems, a set of linear differential matrix inequality conditions is derived based on the given state-space realization. Subsequently, LTV negative imaginary theory is specialized to linear parameter-varying (LPV) cases for which, the differential matrix inequality conditions can easily be avoided by considering the rate of variation of the uncertain parameters as independent LMI variables. Finally, a set of sufficient conditions is derived which ensures that the origin is a globally asymptotically stable equilibrium point of an unforced positive feedback interconnection of two uniformly asymptotically stable LTV negative imaginary systems.

Keywords: Linear systems, Formal Verification/Synthesis, Optimization algorithms
Abstract: Despite the possibility to quickly compute reachable sets of large-scale linear systems, current methods are not yet widely applied by practitioners. The main reason for this is probably that current approaches are not push-button-capable and still require to manually set crucial parameters, such as time step sizes and the accuracy of the used set representation---these settings require expert knowledge. We present a generic framework to automatically find near-optimal parameters for reachability analysis of linear systems given a user-defined accuracy. To limit the computational overhead as much as possible, our methods tune all relevant parameters during runtime. We evaluate our approach on benchmarks from the ARCH competition as well as on random examples. The results show that our new framework verifies the selected benchmarks faster than manually-tuned parameters and is an order of magnitude faster compared to genetic algorithms.

Keywords: Algebraic/geometric methods, Linear systems, Stability of nonlinear systems
Abstract: The paper deals with the characterization of a dummy 'output function' associated with the stable component of the zero-dynamics of a linear square multi-input multi-output system. With reference to the 4-Tank dynamics, it is shown how such a procedure, applied to the linear tangent model of a nonlinear plant, may be profitably applied to assure local stability in closed loop.

Keywords: Estimation, Identification, Linear systems
Abstract: This paper deals with fractional order and the parameter identification of a non-commensurable fractional order system using an iterative method consisting of two steps. The novelty is that the system needs not to be at rest and that an implementable algorithm is given using the Gr?nwald-Letnikov derivative. In the first step of the algorithm, the instrumental variable least-squares method identifies the parameters by means of given values of the fractional orders. To apply the second step, the system is interpreted as a non-linear equation with respect to fractional orders. After setting up a system of equations, one step of Newton's method is performed to improve the estimate of the fractional orders. The required Jacobian as well as a convergence proof of the applied Newton's method is given considering fractional order dependent parameters. Executing both steps iteratively yields the online identification of fractional orders and parameters. A numerical example demonstrating the efficacy of the proposed algorithm concludes the paper.

Keywords: Linear systems, Robust control, LMIs
Abstract: This paper introduces the notion of time-domain output (not necessarily strictly) negative imaginary systems that encompasses all the existing (not only stable) subsets of the negative imaginary systems class. A time-domain dynamic dissipative framework is developed in this paper to describe the full class of output negative imaginary systems (i.e. including systems having poles on the imaginary axis). This dynamic dissipative framework also leads to an LMI-based state-space characterization which can be conveniently used to test the output negative imaginary property of a given LTI system. It is further established that for time-domain output negative imaginary systems, the proposed dynamic dissipative framework is equivalent to the classical dissipative property of this class of systems with respect to the supply rate w(u,dot{bar{y}}). Interestingly, the class of time-domain output strictly negative imaginary systems now captures systems that are not necessarily stable -- it is found that the majority of the SISO, LTI transfer functions with a simple pole at the origin satisfy this property. Numerical examples are provided throughout the paper for better illustration.

Keywords: Linear systems, Behavioural systems, Uncertain systems
Abstract: The main inversion-based control architectures are the plant and closed-loop inversion architectures. For scalar continuous-time linear systems, these architectures are shown to be fully equivalent for both the minimum and nonminimum-phase cases when exact stable inverses are used. This equivalence, deduced by using a behavioral approach, dictates that the two architectures deliver the same performances for any disturbance and mis-modeling affecting the controlled plant. A simulation example highlights that the equivalence still holds in practice when a careful truncation of the preaction control is performed.

Keywords: Stability of linear systems, Linear systems, Uncertain systems
Abstract: We characterize the ?structures? defining a class of real matrices?called nests?given by A in R^n×n such that, up to relabeling, all of its leading principal submatrices indexed by {1,2,...,k} satisfy sgn det A[{1,2,...,k}]=(−1)^k, k≤n. By structure we mean elements of {−1,0,1}^n×n, which circumscribe the signs of realizations within a class of real matrices. We frame the problem of characterizing structures in a form amenable to classic control theory, and that generalizes to any class of matrices defined by potentially Hurwitz structures, such as nests.

Keywords: Stability of linear systems, Distributed control, Decentralized control
Abstract: This paper establishes the essential technique for exponentially stabilizing a jointly controllable, jointly observable, multi-channel linear system at any prescribed convergence rate using a time-invariant distributed linear control. It will be made clear that the well-known fixed spectrum (i.e., the set of fixed modes) of a multi-channel linear system is no longer an obstacle to the effective control of such a system provided that distributed rather than classical decentralized control is used. This is true for both continuous-time and discrete-time systems. Moreover, the effect of transmission delays is also investigated. It will be elucidated why in the face of such delays, exponential stabilization with an arbitrarily fast convergence rate can still be achieved with distributed control, at least for discrete-time multi-channel linear systems.

Keywords: Sampled-data control, Linear systems, Network analysis and control
Abstract: In this paper, the problem of estimating a suitable bound for ensuring multiconsensus of single integrators under asynchronous and aperiodical sampling is investigated. The estimate relies on a hybrid modeling of the network dynamics with a distributed time-delay acting over the connection. Simulations support the theoretical results.

Keywords: Sampled-data control, Numerical algorithms, Learning
Abstract: This paper is concentrated on aperiodic sampling and adaptive learning in continuous-time nonlinear systems. The objective is to find the optimal control policy by minimizing an infinite-quadratic cost function in an online fashion. An algorithm based on integral reinforcement learning is proposed for problems with unknown model information, and a novel dynamic triggering method is combined for saving communication as much as possible. The identifying neural network is utilized to free the input dynamics and critic neural network is constructed to approximate the cost function. The weight convergence, and asymptotic stability of the theoretical results are elaborated and, afterwards, a numerical example is presented for illustrating the effectiveness and superiority of the algorithm by comparison.

Keywords: Networked control systems, Sampled-data control, Linear systems
Abstract: This paper analyzes the evolution of inter-event times for a planar linear system under a general class of scale-invariant event triggering rules. For scale-invariant event triggering rules, the inter-event time is a function of only the "angle" of the state at an event. We analyze the properties of this inter-event time function such as periodicity and continuity. In particular, the inter-event time function is continuous except for finitely many "angles" and we provide sufficient conditions under which the inter-event time function is continuous. Then, we analyze the evolution of the "angle" of the state from one event to the next and reduce the problem of studying the evolution of the inter-event times to that of studying the "angle" map and its fixed points. For a specific triggering rule, we provide necessary conditions for the convergence of inter-event time to a steady state value. We illustrate the proposed results through numerical simulations.

Keywords: Robust control, Predictive control for linear systems, Sampled-data control
Abstract: Leveraging autonomous systems in safety-critical applications requires formal robustness guarantees against uncertainties. We address this issue by computing safe terminal sets with corresponding safety-preserving terminal controllers, which ensure robust constraint satisfaction for an infinite time horizon. To maximize the region of operation, we also construct safe initial sets that are as large as possible and yet can be safely steered into the safe terminal set in finite time. We use scalable reachability analysis and convex optimization to efficiently compute safe sets of sampled-data systems. These systems are composed of a physical plant evolving in continuous-time and a digital controller being implemented in discrete-time. We further verify the effectiveness of our robust control approach using a simple double integrator system and a vehicle platooning benchmark.

Keywords: Switched systems, Lyapunov methods, Networked control systems
Abstract: A relay-explorer control method for nonlinear multi-agent systems is developed to allow a relay agent to intermittently provide navigational feedback to an explorer leader. A distributed controller is developed for formation control and leader tracking for the explorer followers, enabling a multi-agent system to explore an unknown environment indefinitely. To compensate for the lack or inability to use navigational sensors, state observers are used to propagate state estimates for the relay and explorer agents (e.g., in GPS-denied regions). Stabilizing dwell-time conditions are determined via a Lyapunov-based switched systems approach to ensure the trajectory tracking errors are globally uniformly ultimately bounded defined by user-defined thresholds. Using the developed approach, a multi-agent system's trajectory tracking error remains bounded, enabling the exploration of GPS-denied regions for a predetermined period of time, before acquiring navigational feedback from a relay agent.

Keywords: Networked control systems, Robotics, Agents-based systems
Abstract: This paper addresses an actuator-fault-tolerant controller for task-space consensus of networked EulerLagrange systems under time-varying communication delay and switching topology. To account for the discontinuous signals causing by changing topology, we proposed a taskspace reference acceleration based on the signals interchanged intermittently between agents. The velocity reference, obtaining accordingly, is utilized to design a control law for distributed task-space consensus when the actuators are subject to partialloss-of-effectiveness. Moreover, the consensus control for EulerLagrange systems with actuator saturation fault mode is also studied. The stability and convergence of consensus for the networked Euler-Lagrange systems with actuator faults are addressed by the Lyapunov theory and function analysis technique. Numerical examples verify the proposed control schemes? effectiveness and performance with a network of 2-DOF manipulators.

Keywords: Stochastic optimal control
Abstract: We address the problem of steering a stochastic linear system with control-linear noise from an initial condition to a final state while minimizing mean squared deviation from a target state. We assume that the controller can access noiseless, full-state sampled measurements at discrete times. The main contribution is to provide a complete solution to this optimization problem. The explicit properties of the solution are formulated as a Theorem and subsequently proven. We show that the optimal feedback control law is linear in the initial state, the target state, and the sampled measurements. Moreover, we show that the time-varying, matrix-valued feedback state gains can be computed offline before the system is launched. Numerical studies show that the mean squared deviation decreases dramatically as the number of measurements grows and converges to a nonzero limiting value.

Keywords: Vision-based control
Abstract: Image-based control (IBC) systems have a long sensing delay. The advent of multiprocessor platforms helps to cope with this delay by pipelining of the sensing task. However, existing pipelined IBC system designs are based on linear time-invariant models and do not consider constraint satisfaction, system nonlinearities, workload variations and/or given inter-frame dependencies which are crucial for practical implementation. A pipelined IBC system implementation using a model predictive control (MPC) approach that can address these limitations making a step forward towards real-life adaptation is thus promising. We present an adaptive MPC formulation based on linear parameter-varying input/output models for a pipelined implementation of IBC systems. The proposed method maximizes quality-of-control by taking into account workload variations in the image processing for individual pipes in the sensing pipeline in order to exploit the latest measurements, besides explicitly considering given inter-frame dependencies, system nonlinearities and constraints on system variables. The practical benefits are highlighted through simulations using vision-based vehicle lateral control as a case study.

Keywords: Autonomous vehicles, Estimation, Optimization
Abstract: This paper presents a cooperative method to estimate the flow field by a group of autonomous underwater vehicles (AUVs). In this paper, it is assumed that each vehicle can detect the relative positions of its neighboring AUVs during the underwater phase. Since AUVs' trajectories depend on the initially unknown flow field, we define the deviation between the actual and predicted trajectories as the motion-integration error, and the difference of the actual and predicted relative positions between an AUV and its neighbor as the relative motion-integration error. Using these integration errors, a system of nonlinear equations for vehicle trajectories and unknown flow fields is constructed. Then the flow field is estimated by solving an inverse problem for these equations with two different types of error constraints.The convergence of the cooperative estimation algorithm is proved. Finally, simulations are provided to illustrate the effectiveness of the proposed algorithm.

Keywords: Autonomous vehicles, Maritime control, Optimal control
Abstract: Trajectory planning is a central task for operating autonomous underwater vehicles. However, strong disturbances in underwater environments such as currents and waves can cause large deviations between a planned trajectory and the vehicle, resulting in obstacle collision. In this paper, we address this problem by modelling wave disturbances first as a time-varying and position-independent and then as a time-varying and position-dependent function. A Hamilton-Jacobi differential game formulation is then used to compute a value function and level set. Obstacles in an environment are subsequently augmented by this set, and model predictive control is then used for trajectory planning whilst guaranteeing safety. We find that modelling disturbances in this way results in less-conservative safety-guaranteed trajectory planning compared to the case of time-invariant disturbances.

Keywords: Control of networks, Maritime control, Control over communications
Abstract: This work presents a distributed connectivity maintenance algorithm for a multi-agent system consisting of unmanned underwater vehicles (UUVs). The vehicles in the network communicate through a time-division multiple-access (TDMA) protocol, where only one vehicle can broadcast its information at any time instant. The TDMA protocol presents a significant challenge in developing a connectivity maintenance algorithm, as the vehicles do not have access to the present positions of their neighbors. We consider a homogeneous network of UUVs that move in a two-dimensional plane with bounded linear and angular speeds. The algorithm presented here uses only local information from an agent?s neighbors and provides motion constraints, which, if satisfied, ensure the connectivity of the network. We provide mathematical guarantees of network connectivity for the presented algorithm under suitable assumptions on each vehicle?s motion planner and controller. Finally, we present simulation results to demonstrate the effectiveness of the proposed algorithm.

Keywords: Maritime control, Nonholonomic systems, Robust adaptive control
Abstract: This paper considers the 3D path following problem for a class of torpedo-type AUVs (autonomous underwater vehicles), where only three control inputs (surge force, pitch and yaw moments) are available for its 6DoF (degree-of-freedom) motion in the water. For this typical underactuated system, two spherical coordinate transformations are introduced in this paper so as to transform the vehicle's path following model into certain three-input-three-output 2nd-order strict-feedback form. On the other hand, for underwater vehicles, due to their complicate and high nonlinear hydrodynamics, it is difficult to extract all of the exact hydrodynamic coefficients using conventional estimation methods such as CFD (Computational Fluid Dynamics) or PMM (Planar Motion Mechanism) tests. Moreover, considerable noises are unavoidable in the practical sensor measurements. For these reasons, in this paper, a sort of neural-net based on-line estimation method combined with robust scheme is applied to solve the above three-input-three-output strict-feedback form of path following problem. Proposed robust adaptive scheme can guarantee the uniform ultimate boundedness (UUB) of closed-loop system in terms of the spherical coordinates.

Keywords: Robotics, Hybrid systems, Maritime control
Abstract: This paper introduces hysteretic control Lyapunov functions (HCLFs) for hybrid feedback control of a class of continuous-time systems. A family of HCLFs consists of local control Lyapunov functions defined on open domains, and include finite collections of open and closed sets that cover the state-space, implicitly defining a hysteresis-based switching mechanism. Given an HCLF family, we derive sufficient conditions for the existence of globally asymptotically stabilizing hybrid control laws. Moreover, we provide a constructive design procedure for synthesis of optimization-based feedback laws under mild conditions on the objective functions. We construct HCLFs for an underwater vehicle and demonstrate their applicability to hybrid control design for global asymptotic trajectory tracking for underwater vehicles.

Keywords: Autonomous systems, Hybrid systems, Lyapunov methods
Abstract: Robot missions typically involve a number of desired objectives, such as avoiding collisions, staying connected to other robots, gathering information using sensors and returning to the charging station before the battery runs out. Some of these objectives need to be taken into account at the same time, such as avoiding collisions and staying connected, while others are focused upon during different parts of the executions, such as returning to the charging station and connectivity maintenance.

In this paper, we show how Control Barrier Functions(CBFs) and Behavior Trees(BTs) can be combined in a principled manner to achieve both types of task compositions, with performance guarantees in terms of mission completion. We illustrate our method with an underwater coverage mission.

Keywords: Maritime control, Autonomous vehicles
Abstract: The task of maneuvering ships in confined environments is a difficult task for a human operator. One major reason is due to the complex and slow dynamics of the ship which need to be accounted for in order to successfully steer the vehicle. In this work, a two-step optimization-based motion planner is proposed for autonomous maneuvering of ships in constrained environments such as harbors. A lattice-based motion planner is used in a first step to compute a feasible, but suboptimal solution to a discretized version of the motion planning problem. This solution is then used to enable efficient warm-start and as a terminal manifold for a second receding-horizon improvement step. Both steps of the algorithm use a high-fidelity model of the ship to plan feasible and energy-efficient trajectories. Moreover, a novel algorithm is proposed for automatic computation of spatial safety envelopes around the trajectory computed by the lattice-based planner. These safety envelopes are used in the second improvement step to obtain collision-avoidance constraints which complexity scales very well with an increased number of surrounding obstacles. The proposed optimization-based motion planner is evaluated with successful results in a simulation study for autonomous docking problems in a model of the Cape Town~harbor.

Keywords: Maritime control, Learning, Uncertain systems
Abstract: This paper presents a novel model-reference reinforcement learning control method for uncertain autonomous surface vehicles. The proposed control combines a conventional model-based control method with deep reinforcement learning. With the conventional model-based control, we can ensure the learning-based control law provides closed-loop stability for the trajectory tracking control of the overall system, and increase the sample efficiency of the deep reinforcement learning. With reinforcement learning, we can directly learn a control law to compensate for modeling uncertainties. In the proposed control, a nominal system is employed for the design of a baseline control law using a conventional control approach. The nominal system also defines the desired performance for uncertain autonomous vehicles to follow. In comparison with traditional deep reinforcement learning methods, our proposed learning-based control can provide stability guarantees and better sample efficiency. We demonstrate the performance of the new algorithm via extensive simulation results.

Keywords: Nonholonomic systems, Control applications
Abstract: In this paper we consider the asymptotic behaviour and the trajectory generation problem for the Chaplygin sleigh interacting with a potential fluid. We investigate which trajectories can be obtained, at least asymptotically as t tents to infinity, by controlling some of the coordinates (shape--control system) and using the theory of reconstruction. Moreover we support our conclusions via numerical simulations.

Keywords: Cooperative control, Nonholonomic systems
Abstract: This work investigates the effects of adapting decentralized gradient-based control laws to nonholonomic agents in networked formation systems. Using the unicycle agent model and a standard cascade control structure, it is shown that the stability margins of the cascaded systems deteriorate as the numbers of agents increase. This trend indicates problems with both convergence and scalability. It is then shown that the asymptotic behaviors of the nominal gradient-based control laws can be recovered by introducing a bump function that allows forward motion only when the agents are oriented in appropriate directions. The proposed solution ensures almost global convergence and can be applied to formation systems of all sizes. Finally, comprehensive simulation results show that the usage of a bump function also reduces the total energy consumption required to reach a target formation.

Keywords: Cooperative control, Sensor networks, Optimization
Abstract: This paper investigates control design for the coverage problem using mobile sensors, which have nonlinear dynamics with non-smooth directional sensing ranges.Different from the standard gradient based optimization technique to find the optimal coverage problem in literature, new control methodology is needed to compute the gradient of non-smooth cost function and ensure the convergence.In this approach, the boundaries of sensing range are approximated by smooth sigmoid functions, leading to an approximation of the coverage cost function.With this approximation, an innovative non-smooth gradient-based coverage controller is designed for mobile sensors with nonlinear unicycle dynamics.Our work shows that once the initial state of sensors is within the set where the gradient of the approximated cost function is well-defined, the state of sensors will stay in this set and will converge to an invariant set, which contains all critical points (or optimal solutions) of the coverage problem. Simulation results verify the effectiveness of the proposed coverage control approach.

Keywords: Robotics, Networked control systems, Cooperative control
Abstract: The persistent coverage control problem is solved in a decentralized fashion for a multi-robot team with limited sensing capability and loss of awareness over time. Each agent in the multi-robot team possesses a measure of awareness about the environment, encoded as time-varying density functions. The team is tasked with increasing their awareness of the domain in a decentralized way while coordinating with neighboring agents to maintain coverage over the entire domain. Local exchanges of awareness levels between neighbors is shown to allow awareness information over the entire domain to propagate to all agents with performance guarantees. A control law is proposed to obtain (locally) optimal coverage, and a bound of number of robots for guaranteed loss of awareness of the domain is provided. The proposed control law is verified in silico for a team of nonholonomic planar robots.

Keywords: Modeling, Robotics, Optimization
Abstract: Flapping wing flight is a challenging dynamical problem and is also a very fascinating subject to study in the field of biomimetic robotics. A Bat, in particular, has a very articulated arm-wing mechanism with high degrees-of-freedom and flexibility which allows the animal to perform highly dynamic and complex maneuvers, such as upside-down perching. This paper presents the derivation of a multi-body dynamical system of a bio-inspired bat robot called Aerobat which captures multiple biologically meaningful degrees-of-freedom for flapping flight that is present in biological bats. Then, the work attempts to manifest closed-loop aerial body reorientation and preparation for landing through the manipulation of inertial dynamics and aerodynamics by enforcing nonholonomic constraints onto the system. The proposed design paradigm assumes for rapidly exponentially stable controllers that enforce holonomic constraints in the joint space of the model. A model and optimization-based nonlinear controller is applied to resolve the joint trajectories such that the desired angular momentum about the roll axis is achieved.

Keywords: Decentralized control, Nonholonomic systems, Constrained control
Abstract: We solve the full-consensus problem (in position and orientation) with connectivity maintenance for multiple nonholonomic vehicles in a leader-follower configuration. We rely on a polar-coordinates based model which is more natural for the problem setting. The proposed control law is smooth (in the domain of definition) time-invariant and uses only relative measurements, making it more suited for implementation. We establish asymptotic convergence to the consensus manifold as well as connectivity maintenance using the Lyapunov?s first method and cascaded systems theory. In addition, we illustrate our theoretical contributions experimentally.

Keywords: Nonholonomic systems, Network analysis and control, Lyapunov methods
Abstract: We address the problem of consensus control of second-order nonholonomic systems via distributed control under the assumption that each vehicle receives measured states from a set of neighbors, with a bounded, time-varying, but non-differentiable delay. The controller that we propose guarantees full consensus, in the sense that a common consensus point may be reached both in the Cartesian positions on the plane and the orientations of all robots referred to a fixed frame. Our controller is smooth, hence time-varying. Notably, it relies on a property of persistency of excitation. Our main statement guarantees uniform global asymptotic stability. Also, we provide some simulation results to illustrate our theoretical findings.

Keywords: Numerical algorithms, Nonholonomic systems, Autonomous systems
Abstract: This paper presents a mathematical analysis of the velocity obstacle algorithm applied to a nonholonomic vehicle for avoiding a moving obstacle in the plane. The velocity obstacle algorithm can be used for local navigation among dynamic obstacles by continually computing a set of unsafe velocities, and avoid the velocities inside of this set. The method is commonly used for reactive collision avoidance as it requires only limited knowledge of the obstacle behaviour and is computationally inexpensive. A drawback of previous analyses is the assumption that the vehicle and the obstacle are constrained to follow specific types of paths, or the velocities are assumed constant. We analyze the algorithm without such constraints and derive a set of conditions to prove that vehicle safety can be guaranteed in the general case. Moreover, we prove that the method can safely be applied to vehicles subject to nonholonomic constraints, with limited turning rates.

Keywords: Cooperative control, Networked control systems, Autonomous vehicles
Abstract: This paper investigates the problems of consensus in networks of nonlinear integrators, as well as the coordinated path following control of multiple fixed-wing unmanned aerial vehicles (UAVs). Firstly, by employing the notions related to reduction theorem, it is shown that the classic consensus protocol is still effective for networks of nonlinear integrators, which are the nonlinear generalization of integrators with bounded inputs. The requirement to achieve consensus is still that the underlying digraphs contain directed spanning trees. Then the results are employed to design a novel coordinated path following control law for heterogeneous fixed-wing UAVs with control input constraints. Asymptotic stability of the closed-loop system is theoretically guaranteed, as long as the requirement for consensus is satisfied.

Keywords: Agents-based systems, Cooperative control, Decentralized control
Abstract: In this paper, we consider the optimisation of time varying functions by a network of agents with no gradient information. We propose a novel method to estimate the gradient at each agent's position using only neighbour information. The gradient estimation is coupled with a formation controller, to minimise gradient estimation error and prevent agent collisions. Convergence results for the algorithm are provided for functions which satisfy the Polyak-Lojasiewicz inequality. Simulations and numerical results are provided to support the theoretical results.

Keywords: Cooperative control, Agents-based systems
Abstract: This paper presents two communication-efficient distributed algorithms for solving linear algebraic equations of the form Ax = b, which has at least one solution, among a network of m>1 agents. Each agent knows only a subset of the rows of the partitioned matrix [A b] and recursively updates its estimate of a solution by utilizing information received only from its neighbors. Neighbor relations are characterized by a fixed directed graph. The first algorithm aims to reduce communication costs at each iteration, in which each agent broadcasts the entries of its estimate in a cyclic manner, instead of broadcasting the entire vector of its estimate. It is shown that for any strongly connected neighbor graph, the algorithm causes all agents' estimates to converge to the same solution to Ax=b exponentially fast. The second algorithm reduces the vector size of each agent's estimate by exploiting the sparsity of the matrix A. It is shown that the algorithm causes each agent's estimate to converge to a specific part of the same solution to Ax=b corresponding to its own interest exponentially fast for a certain class of directed graphs.

Keywords: Cooperative control, Autonomous robots, Networked control systems
Abstract: We consider the problem of manipulating an unknown payload using multiple agents. The objective is to find both optimal grasping positions and input forces for agents to apply so that the resulting linear and angular velocities make the rigid object track a reference. The associated optimization problem is split into force and position subproblems. The primal?dual gradient dynamics for the force subproblem can be completely decoupled into local dynamics that each agent can implement using only local measurements. The proximal gradient dynamics for the position subproblem require only local object shape information and relative positions between adjacent agents. We prove that combining the optimization dynamics for these subproblems yields an algorithm that converges to a locally optimal point for the joint force-position problem, and provide numerical simulations that demonstrate its performance on practical problems.

Keywords: Cooperative control, Autonomous robots
Abstract: This paper studies a defense approach against one or more swarms of adversarial agents. In our earlier work, we employ a closed formation (`StringNet') of defending agents (defenders) around a swarm of adversarial agents (attackers) to confine their motion within given bounds, and guide them to a safe area. The control design relies on the assumption that the adversarial agents remain close enough to each other, i.e., within a prescribed connectivity region. To handle situations when the attackers no longer stay within such a connectivity region, but rather split into smaller swarms (clusters) to maximize the chance or impact of attack, this paper proposes an approach to learn the attacking sub-swarms and reassign defenders towards the attackers. We use a `Density-based Spatial Clustering of Application with Noise (DBSCAN)' algorithm to identify the spatially distributed swarms of the attackers. Then, the defenders are assigned to each identified swarm of attackers by solving a constrained generalized assignment problem. Simulations are provided to demonstrate the effectiveness of the approach.

Keywords: Cooperative control, Autonomous systems, Aerospace
Abstract: A reach-avoid differential game with multiple players is considered in this paper. A group of defenders is in charge of capturing a spy before it leaves the game set. This paper addresses cooperation among the defenders which protect a circular area on interest and try to intercept an intelligent adversary/intruder. The optimal strategies for each team, the defenders team and the spy, are obtained. These strategies and the Value function are obtained in analytical and explicit form. Furthermore, it is verified that the Value function is continuously differentiable and it is the solution of the Hamilton-Jacobi-Isaacs equation. Finally, the Barrier surface that separates the winning regions of each team is explicitly obtained as well. Illustrative examples show the Barrier surface cross-sections of this high dimensional differential game.

Keywords: Cooperative control, Human-in-the-loop control, Modeling
Abstract: This paper introduces a continuous-time incomplete information game to model the negotiation process of human-machine cooperative decision making called the n-stage war of attrition. It extends the scope of the conventional war of attrition to describe incomplete information coordination settings among two players with more than two different action options and with a time-dependent cost function. At each stage of the game, players try to outlast each other facing the trade-off between increasing disagreement costs and valuation difference between the currently chosen action to the next highest valuated action. The required number of stages for reaching the agreement on one decision option is unknown throughout the game. The proposed solution strategy is a formalism to determine the thresholds for conceding which maximize the expected payout w.r.t. the valuation difference density function of the other player. We prove that the associated symmetric strategy profile leads to a perfect Bayesian equilibrium. Towards the designated application of the n-stage war of attrition, this work also addresses the inverse game problem. We introduce an identification method to estimate the opponent?s valuation difference density function and provide results that document the identification ability.

Keywords: Observers for nonlinear systems, Predictive control for nonlinear systems
Abstract: The present work provides two alternatives to formulate time-discounted incremental input/output-to-state stability (i-IOSS) as a suitable detectability notion for general nonlinear systems with non-additive disturbances. Both formulations are related to existing i-IOSS notions which result as special cases. Previous results that provide a sufficient Lyapunov-function condition for i-IOSS and that prove i-IOSS to be necessary for the existence of robustly stable full-order state observers are generalized to the presented time-discounted i-IOSS definition for general nonlinear systems. For linear systems, explicit i-IOSS bounds are presented.

Keywords: Observers for nonlinear systems, Algebraic/geometric methods, Feedback linearization
Abstract: The kinematics of many mechanical systems encountered in robotics and other fields, such as single-bearing attitude estimation and SLAM, are naturally posed on homogeneous spaces: That is, their state lies in a smooth manifold equipped with a transitive Lie-group symmetry. This paper shows that any system posed in a homogeneous space can be extended to a larger system that is equivariant under a symmetry action. The equivariant structure of the system is exploited to propose a novel new filter, the Equivariant Filter (EqF), based on linearisation of global error dynamics derived from the symmetry action. The EqF is applied to an example of estimating the positions of stationary landmarks relative to a moving monocular camera that is intractable for previously proposed symmetry based filter design methodologies.

Keywords: Observers for nonlinear systems, Uncertain systems, LMIs
Abstract: Novel discrete-time (DT) state observers and unknown input estimators are proposed for a class of DT nonlinear systems whose nonlinearity can be characterized by incremental multiplier matrices. The inputs to the nonlinear systems are allowed to have an unknown component. These nonlinear models are represented as linear models by treating the nonlinearity as a nonlinear input with a known structure. A novel DT state observer is proposed and a condition for its existence is given in terms of a linear matrix inequality (LMI). The unknown input estimator estimates the system unknown input with one sampling period time-delay. Unknown input estimators for continuous-time (CT) systems using their DT plant models are proposed. The proposed state observer and unknown input estimator are tested on numerical examples. An application of the proposed unknown input estimator to reconstruct malicious packet drops during the control signal transmission is given.

Keywords: Feedback linearization, Observers for nonlinear systems
Abstract: Recently, Freidovich and Khalil have shown that a nonlinear system having relative degree n and a stable zero dynamics can be controlled, by means of an extended high-gain observer, so as to recover ? up to any arbitrarily fixed degree of accuracy ? the performance that would have been obtained by means of the classical feedback-linearization design. This observer involves a gain parameter that grows up to power n+1. In this paper we show that the same result can be obtained by means of a controller employing an extension of ?low power? high-gain observer of Astolfi and Marconi, in which the gain parameter grows up only to power 2.

Keywords: Observers for nonlinear systems, Fluid flow systems, Estimation
Abstract: Vortex shedding in the turbulent wake of a square cylinder is modeled by a minimal generalized empirical Galerkin model (GM). Pressure measurements on the sides and on the back of the bluff body are used as a system output to rebuild the system full state. Despite a large number of unresolved states and the intermittent character of the vortex shedding, the use of an observer makes possible the estimation of the shift mode and the growth rate of the dynamic model truncated at order two. A high gain observer is synthesized and both simulation and experimental results show promising applications for the feedback control of the vortex shedding in order to decrease the drag coefficient, even in the case of a turbulent wake flow at high Reynolds numbers.

Keywords: Observers for nonlinear systems
Abstract: This paper deals with the observation of the wake flow behind a bluff body based on reduced order models. Two Galerkin models with different truncation orders are considered to capture the intermittent character of the vortex shedding. The system output is the oscillation amplitude obtained thanks to pression measurements on the sides and on the back of the bluff body. For flow control purposes, the state estimation has to be efficient and robust to noises and dynamic changes. A high gain observer is modified i) by extending the state with the introduction of fictitious outputs in order to avoid an observability singularity and to ensure the existence of the inverse jacobian matrix and ii) by integrating a high gain parameter whose power is limited to 2 instead of n to address the sensitivity issue of the standard high gain observer. Simulation results illustrate the efficiency of the proposed observers and highlight promising applications for flow control at high Reynolds numbers.

Keywords: Observers for nonlinear systems, Numerical algorithms, Neural networks
Abstract: In this paper, we propose a method to numerically design observers for nonlinear system. The method relies on the theory of Luenberger observers, which consist in mapping the nonlinear dynamics to a linear system, for which observer design is easy. Relying on results guaranteeing the existence of such mappings, we propose to approximate them by performing nonlinear regression on data simply generated by solving the system and observer dynamics. We detail different approaches for autonomous and excited systems and the choices made for data generation, pre-processing, and regression.

Keywords: Observers for nonlinear systems, Fault diagnosis
Abstract: A simultaneous input and state interval observer is presented for Lipschitz continuous nonlinear systems with unknown inputs and bounded noise signals for the case when the direct feedthrough matrix has full column rank. The observer leverages the existence of bounding decomposition functions for mixed monotone mappings to recursively compute the maximal and minimal elements of the estimate intervals that are compatible with output/measurement signals, and are proven to contain the true state and unknown input. Furthermore, we derive a Lipschitz-like property for decomposition functions, which provides several sufficient conditions for stability of the designed observer and boundedness of the sequence of estimate interval widths. Finally, the effectiveness of our approach is demonstrated using an illustrative example.

Keywords: Control Systems Privacy, Cyber-Physical Security, Behavioural systems
Abstract: Control as a Service (CaaS) is becoming a reality?particularly in the case of building automation and smart grid management. Often, the control algorithms in CaaS focus on controlling the client's system directly from input-output data, since the system's model might be private or unavailable. Therefore, large quantities of data collected from the client need to be uploaded to a cloud server. This data can be used by a malevolent cloud service provider to infer sensitive information about the client and mount attacks. In this paper, we co-design a solution that interlaces control and privacy. Our goal is to perform online data-driven control on encrypted input-output data, while maintaining the privacy of the client's uploaded data, desired setpoint and control actions. We design our control algorithm based on results from the behavioral framework, which is more encryption-friendly compared to other classical frameworks. We obtain privacy by using a leveled homomorphic encryption scheme to enable the cloud to perform complex computations on the client's encrypted data. Finally, we achieve efficiency by manipulating the tasks required by the control algorithm such that they only involve arithmetic circuits, as well as by leveraging parallelization and ciphertext packing.

Keywords: Sensor fusion, Estimation, Kalman filtering
Abstract: Fast covariance intersection is a widespread technique for state estimate fusion in sensor networks when cross-correlations are not known and fast computations are desired. The common requirement of sending estimates from one party to another during fusion forfeits local privacy. Current secure fusion algorithms rely on encryption schemes that do not provide sufficient flexibility. As a result, excess communication between estimate producers is required, which is often undesirable. We propose a novel method of homomorphically computing the fast covariance intersection algorithm on estimates encrypted with a combination of encryption schemes. Using order revealing encryption, we show how an approximate solution to the fast covariance intersection weights can be computed and combined with partially homomorphic encryptions of estimates, to calculate an encryption of the fused result. The described approach allows secure fusion of any number of private estimates, making third-party cloud processing a viable option when working with sensitive state estimates or when performing estimation over untrusted networks.

Keywords: Computer/Network Security, Control Systems Privacy, Cyber-Physical Security
Abstract: The design of encrypted controllers, which perform control operation directly over encrypted signals via homomorphic cryptosystems, should consider both security of the control data and performance of the controller. Considering the use of Learning With Errors (LWE) based cryptosystem, in this paper, we present a design procedure for encrypted linear dynamic controllers. Providing a guideline for choosing the parameters of the cryptosystem as well as quantization, the procedure guarantees both the desired level of security and performance. Receiving the encrypted signals of the plant input as well as the output, the proposed controller is able to perform the dynamic operation over encrypted data for infinite time horizon, without the use of decryption or reset of the state. Thanks to additively and multiplicatively homomorphic property of the LWE-based cryptosystem, information of both control signals and gain matrices is protected by encryption.

Keywords: Control Systems Privacy, Cyber-Physical Security, Predictive control for linear systems
Abstract: Encrypted control enables confidential controller evaluations in cloud-based or networked control systems. From a technical point of view, an encrypted controller is a modified control algorithm that is capable of computing encrypted control actions based on encrypted system states (without decrypting the states). A key technology for the design of encrypted controllers is homomorphic encryption that allows simple mathematical operations to be carried out on encrypted data. As apparent from existing schemes, one of the main challenges in encrypted control is to reformulate given control laws such that they can be merged with these special cryptosystems.

In this paper, a novel encrypted implementation of model predictive control (MPC) is presented. We utilize that MPC for linear systems with polytopic constraints is well known to result in a continuous piecewise affine (PWA) control law. Thus, we can apply techniques for the decomposition of PWA functions into two convex PWA parts. The convexity of the decomposed parts finally allows us to realize a secure two-party evaluation of the original PWA function and, hence, of explicit~MPC. Compared to existing encrypted MPC schemes, the novel approach makes significantly better use of computational resources offered by the two involved clouds.

Keywords: Cyber-Physical Security, Quantized systems, Networked control systems
Abstract: This study considers a quantizer design problem of an encrypted control system with a dynamic feedback controller. Controller parameters and signals over network links are concealed by ElGamal encryption, which is multiplicative homomorphic encryption. The encryption scheme allows direct evaluation of multiplication by using encrypted data. The proposed dynamic quantizer has a time-varying sensitivity updated by the magnitude of plant outputs and observer states. Further, it ensures asymptotic stability of the Luenberger observer in an encrypted fashion and a closed-loop system simultaneously. A numerical example demonstrates that the proposed dynamic quantizer achieves asymptotic stability and improves the control performance of the encrypted control system with a regulator.

Keywords: Control Systems Privacy, Cyber-Physical Security
Abstract: For a class of Cyber-Physical Systems (CPSs), we address the problem of performing computations over the cloud without revealing private information about the structure and operation of the system. We model CPSs as a collection of input-output dynamical systems (the system operation modes). Depending on the mode the system is operating on, the output trajectory is generated by one of these systems in response to driving inputs. Output measurements and driving inputs are sent to the cloud for processing purposes. We capture this ``processing'' through some function (of the input-output trajectory) that we require the cloud to compute accurately -- referred here as the trajectory utility. However, for privacy reasons, we would like to keep the mode private, i.e., we do not want the cloud to correctly identify what mode of the CPS produced a given trajectory. To this end, we distort trajectories before transmission and send the corrupted data to the cloud. We provide mathematical tools (based on output-regulation techniques) to properly design distorting mechanisms so that: 1) the original and distorted trajectories lead to the same utility; and the distorted data leads the cloud to misclassify the mode.

Keywords: Cyber-Physical Security, Resilient Control Systems, Networked control systems
Abstract: In recent years, the integration of encryption schemes into cyber-physical systems (CPS) has attracted much attention to improve the confidentiality of sensor signals and control input signals sent over the network. However, in principle an adversary can still modify the sensor signals and the control input signals, even though he does not know the concrete values of the signals. In this paper, we shall first show that a standard encryption scheme can not prevent some sophisticated attacks such as covert attacks, which remain invisible in the CPS with encrypted communication and a conventional diagnosis system. To cope with this problem, an improved encryption scheme is proposed to mask the communication and to cancel the influence of the attack signal out of the system. The basic idea is to swap the plaintext and the generated random value in the somewhat homomorphic encryption (SWHE) scheme to prevent a direct access of the adversary to the transmitted plaintext. It will be shown that the CPS with the improved encryption scheme is resilient to covert attacks. The proposed encryption scheme and the CPS structure are finally illustrated through the well-established quadruple-tank process.

Keywords: Control Systems Privacy, Distributed control, Cyber-Physical Security
Abstract: This paper presents a distributed algorithm for additive aggregation over encrypted data. Our algorithm allows networked systems to compute the sum of all individual data without revealing each node's private contribution. To conceal the private data, the local computations on each node and the communications with neighbor nodes are conducted by utilizing the additively homomorphic cryptosystem. As a consequence, the leader node which has the secret key of the cryptosystem recovers the correct outcome after decryption in a finite time. Moreover, the leader cannot learn the private data of the other nodes. Furthermore, the proposed algorithm can operate on encrypted data for an infinite time horizon even when the network varies intermittently with time.

Keywords: Automotive control, Closed-loop identification, Neural networks
Abstract: We consider the problem of supervised learning of a multi-model based controller for non-linear systems. Selected multiple linear controllers are used for different operating points and combined with a local weighting scheme, whose weights are predicted by a deep neural network trained online. The network uses process and model outputs to drive the controller towards a suitable mixture of operating points.

The proposed approach, which combines machine learning and classical control of linear processes, allows efficient implementation on complex industrial processes. In this work, the control problem consists in the design of a controller for a waste heat recovery system (WHRS) mounted on a heavy duty (HD) truck engine to decrease fuel consumption and meet the future pollutant emissions standard. Note that the contribution of this work is not specific to HD truck processes since it can be applied to any nonlinear system with an existing linear controller bank.

The proposed control scheme is successfully evaluated on an Organic Rankine Cycle (ORC) process simulator and compared to a standard linear controller and to several strong multi-model baselines without learning.

Keywords: Lyapunov methods, Control applications, Robust control
Abstract: This paper presents a nonlinear control method, which achieves simultaneous fluid flow velocity control and limit cycle oscillation (LCO) suppression in a flexible airfoil. The proposed control design is based on a dynamic model that incorporates the fluid structure interactions (FSI) in the airfoil. The FSI describe how the flow field velocity at the surface of a flexible structure gives rise to fluid forces acting on the structure. In the proposed control method, the LCO are controlled via control of the flow field velocity near the surface of the airfoil using surface-embedded synthetic jet actuators. Specifically, the flow field velocity profile is driven to a desired time-varying profile, which results in a LCO-stabilizing fluid forcing function acting on the airfoil. A Lyapunov-based stability analysis is used to prove that the active flow control system asymptotically converges to the LCO-stabilizing forcing function that suppresses the LCO. Numerical simulation results are provided to demonstrate the performance of the proposed active flow-and-LCO suppression method.

Keywords: Flexible structures, Control applications, Linear systems
Abstract: This paper puts forward an approach to the synthesis of open-loop input shapers via the solution to a general L2 preview tracking problem with FIR constraints on the controller and the error system. This formulation results in a closed-form solution, which is numerically stable to calculate and easy to tune. The approach is experimentally validated on a four-mass laboratory testbed. It is shown to be advantageous to replace the control penalty in the cost with a penalty on the mechanical power of the system.

Keywords: MEMs and Nano systems, Optimal control, Machine learning
Abstract: We address the problem of 2D position control of micro-objects (chiplets) immersed in fluid. An electric field, shaped by an array of electrodes, is used to transport and position chiplets using dielectrophoretic forces. We use a lumped, 2D, capacitive based (nonlinear) motion model to first learn a bi-modal control policy. The learning process is based on optimization featuring automatic differentiation. Next we formally prove that this policy can be generalized. The spatial dependency of the capacitances are estimated using detailed electrostatic COMSOL simulations. The results shown in this paper show that the realization of a system that can digitally convert a design directly to a physical placement of micro-chips is feasible.

Keywords: Process Control, MEMs and Nano systems, Machine learning
Abstract: Elucidating electrostatic surface potentials contributes to a deeper understanding of the nature of matter and its physicochemical properties, which is the basis for a wide field of applications. Scanning quantum dot microscopy, a recently developed technique allows to measure such potentials with atomic resolution. For an efficient deployment in scientific practice, however, it is essential to speed up the scanning process. To this end we employ a two-degree-of-freedom control paradigm, in which a Gaussian process is used as the feedforward part. We present a tailored online learning scheme of the Gaussian process, adapted to scanning quantum dot microscopy, that includes hyperparameter optimization during operation to enable fast and precise scanning of arbitrary surface structures. For the potential application in practice, the accompanying computational cost is reduced evaluating different sparse approximation approaches. The fully independent training conditional approximation, used on a reduced set of active training data, is found to be the most promising approach.

Keywords: Robotics, Control applications, Robust adaptive control
Abstract: In this paper, we present an online adaptive robust control framework for underactuated brachiating robots traversing flexible cables. Since the dynamic model of a flexible body is unknown in practice, we propose an indirect adaptive estimation scheme to approximate the unknown dynamic effects of the flexible cable as an external force with parametric uncertainties. A boundary layer-based sliding mode control is then designed to compensate for the residual unmodeled dynamics and time-varying disturbances, in which the control gain is updated by an auxiliary direct adaptive control mechanism. Stability analysis and derivation of adaptation laws are carried out through a Lyapunov approach, which formally guarantees the stability and tracking performance of the robot-cable system. Simulation experiments and comparison with a baseline controller show that the combined direct-indirect adaptive robust control framework achieves reliable tracking performance and adaptive system identification, enabling the robot to traverse flexible cables in the presence of unmodeled dynamics, parametric uncertainties and unstructured disturbances.

Keywords: Manufacturing systems and automation, Estimation, Intelligent systems
Abstract: Automated measurement of the machine reliability parameters for a production system enables a continuous update of the mathematical model of the system, which can be used for various analysis and productivity improvement. However, the continuous update may be impeded by some machines of which automated parameter measurements are out of order. Such a situation has been observed, for instance, when some of the machines in the line cannot save log files, or IoT devices that measure these machines stop functioning. In this context, this paper addresses the problem of estimating the efficiencies of those machines while avoiding a direct manual measurement (by human) of up- and down times for them. It turns out that those efficiencies can be computed using starvation/blockage data of the neighboring machines along with the system information. With this, a continuous update of the model is possible even though some machines do not report status in automated manner. The method is indirect as opposed to a direct manual measurement by human. The results are derived for serial production lines with Bernoulli reliability characteristics. Simulation studies are carried out to verify the accuracy of proposed estimation method in both two-machine line case and multi-machine line case.

Keywords: Manufacturing systems and automation, Predictive control for nonlinear systems, Constrained control
Abstract: The problem of real-time control and optimization of components' routing in discrete manufacturing plants is considered. This problem features a large number of discrete control inputs and the presence of temporal-logic constraints. A new approach is proposed, with a shift of perspective with respect to previous contributions, from a Eulerian system model that tracks the state of plant nodes, to a Lagrangian model that tracks the state of each part being processed. The approach features a hierarchical structure. At a higher level, a predictive receding horizon strategy allocates a path across the plant to each part in order to minimize a chosen cost criterion. At a lower level, a path following logic computes the control inputs in order to follow the assigned path, while satisfying all constraints. The approach is tested here in simulations, reporting extremely good performance as measured by closed-loop cost function values and computational efficiency.

Keywords: Network analysis and control, Randomized algorithms
Abstract: In this paper, we study the influence of additive noise in randomized consensus algorithms. Assuming that the update matrices are symmetric, we derive a closed form expression for the mean square error induced by the noise, together with upper and lower bounds that are simpler to evaluate. Motivated by the study of Open Multi-Agent Systems, we concentrate on Randomly Induced Discretized Laplacians, a family of update matrices that are generated by sampling subgraphs of a large undirected graph. For these matrices, we express the bounds by using the eigenvalues of the Laplacian matrix of the underlying graph or the graph's average effective resistance, thereby proving their tightness. Finally, we derive expressions for the bounds on some examples of graphs and numerically evaluate them.

Keywords: Network analysis and control, Robust control, Networked control systems
Abstract: A link addition problem is considered for a directed network in order to improve the network robustness. The robustness of network is quantified through a well-known measure of stability margin. Optimal identification of links such that the stability margin is maximized by their addition, requires solving a complex combinatorial problem. Here two efficient methods are proposed for suboptimal link addition by exploiting the sensitivity being embedded in the derivative of singular value and Lagrange multiplier. Numerical tests are presented to demonstrate the efficacy of the proposed methods.

Keywords: Network analysis and control, Distributed control, Adaptive control
Abstract: This paper studies interconnected systems (nodes) and exploits dissipation inequalities and the structure of the interconnection (the network) to derive analysis and design tools for stabilization. First, systems with quadratic supply rates in the dissipation inequalities are investigated. A stability condition based on the dissipation inequality associated to each node is given. This condition allows checking the sign of the dissipation inequality for the overall network system. By considering the underlying directed graph, the feasibility of controller design is discussed. The design problem is re-formulated into the problem of finding a solution to a system of linear inequalities. This allows the efficient search and computation of the design parameters of what we call active nodes. Then, systems with non-quadratic supply rates are considered. A vector of positive definite functions that is used as a basis of the non-quadratic supply rates is constructed: this requires augmenting the underlying directed graph. Similarly to the quadratic supply rates case, a stability condition for analysis and a graph-based criterion for checking the feasibility of controller design are discussed. Finally a design example to demonstrate how to exploit the so-called active nodes to design a controller without numerical computation is presented. The proposed method does not presume any stability property of the nodes and therefore can be applied to various scenarios occurring in the study of stability properties for network systems.

Keywords: Network analysis and control, Networked control systems
Abstract: This work studies the herdability of networked systems. As an extension of classical controllability, herdability represents the ability of a system to drive its states to a specific subset in the state space. Particularly, a leader-follower signed network is considered, where leader nodes endowed with external controls are able to influence the states of the follower nodes. Weighted positive and negative edges are allowed to capture cooperative and competitive interactions among nodes. To enable network herdability, leader group selection is investigated in this work, i.e., identifying a small subset of nodes as leaders such that the resulting leader-follower network is herdable by the selected leaders. Focusing on structurally balanced signed networks, graph walks are leveraged to facilitate leader selection for network herdability. The cases of selecting leaders from the same partitioned set and different sets are considered, which are then extended to a special class of weakly balanced signed graphs. Examples are provided to illustrate the developed leader selection approaches.

Keywords: Network analysis and control, Subspace methods, Large-scale systems
Abstract: Modern infrastructures such as transportation and communication networks are large-scale systems with complex dependence structures between various sub-systems. Human-interpretable performance targets in such systems are often represented in terms of lower-dimensional projections of the high-dimensional state space. We consider the problem of designing control strategies for high-dimensional systems that lack a detailed model. To do so, we leverage the ability of copulas to represent dependant structures in high-dimensional data, and approximate the state space model through inverse sampling. We demonstrate the applicability of the control policies obtained from our methodology through a data-driven case study of controlling flight delays within the US air transportation network.

Keywords: Network analysis and control
Abstract: This paper presents graph theoretic conditions for the controllability and accessibility of bilinear systems over the special orthogonal group and the general linear group, respectively, in the presence of drift terms. Such bilinear systems naturally induce two interaction graphs: one graph from the drift, and another from the controlled dynamics. As a result, the system controllability or accessibility becomes a property of the two graphs in view of the classical Lie algebra rank condition. We establish a systemic way of transforming the Lie bracket operations in the underlying Lie algebra, into specific operations of removing or creating links over the drift and controlled interaction graphs. As a result, we establish a series of graphical conditions for the controllability and accessibility of such bilinear systems, which rely only on the connectivity of the union of the drift and controlled interaction graphs. We present examples to illustrate the validity of the established results, and show that the proposed conditions are in fact considerably tight.

Keywords: Network analysis and control, Game theory, Learning
Abstract: We study the formation of a subscription network where a continuum of strategic, Bayesian subscribers decide to subscribe to one of two sources (leaders) for news that is informative about an underlying state of the world. The leaders, aiming to maximize the welfare of all subscribers, have a motive to persuade the subscribers to take the optimal binary action against the state according to their own perspectives. With this persuasion motive, each leader decides whether to disclose the news to her own subscribers when there is news. When the subscribers receive the news, they update their beliefs; more importantly, even when no news is disclosed, the subscribers update their beliefs, speculating that there may be news that was concealed due to the leader?s strategic disclosure decision. We prove that at any equilibrium, the set of news signals that are concealed by the leaders takes the form of an interval. We further show that when two leaders represent polarized and opposing perspectives, anti-homophily emerges among the subscribers whose perspectives are in the middle. For any subscriber with a perspective on the extremes, and for any leader, there exists an equilibrium at which the subscriber would follow the leader. Our results shed light on how individuals would seek information when information is private or costly to obtain, while considering the strategic disclosure by the news providers who are partisan and have a hidden motive to persuade their followers.

Keywords: Network analysis and control, Communication networks, Sensor networks
Abstract: Inhomogeneous random K-out graphs were recently introduced to model heterogeneous sensor networks secured by random pairwise key predistribution schemes. First, each of the n nodes is classified as type-1 (respectively, type-2) with probability 0

Keywords: Distributed control, Predictive control for linear systems, Optimal control
Abstract: We present the Distributed and Localized Model Predictive Control (DLMPC) algorithm for large-scale structured linear systems, a distributed closed loop model predictive control scheme wherein only local state and model information needs to be exchanged between subsystems for the computation and implementation of control actions. We use the System Level Synthesis (SLS) framework to reformulate the centralized MPC problem as an optimization problem over closed loop system responses, and show that this allows us to naturally impose localized communication constraints between sub-controllers. We show that the structure of the resulting optimization problem can be exploited to develop an Alternating Direction Method of Multipliers (ADMM) based algorithm that allows for distributed and localized computation of distributed closed loop control policies. We conclude with numerical simulations to demonstrate the usefulness of our method, in which we show that the computational complexity of the subproblems solved by each subsystem in DLMPC is independent of the size of the global system. To the best of our knowledge, DLMPC is the first MPC algorithm that allows for the scalable distributed computation of distributed closed loop control policies.

Keywords: Distributed control, Predictive control for linear systems, Optimal control
Abstract: An explicit Model Predictive Control algorithm for large-scale structured linear systems is presented. We base our results on Distributed and Localized Model Predictive Control (DLMPC), a closed loop model predictive control scheme based on the System Level Synthesis (SLS) framework wherein only local state and model information needs to be exchanged between subsystems for the computation and implementation of control actions. We provide an explicit solution for each of the subproblems resulting from the distributed MPC scheme. We show that given the separability of the problem, the explicit solution is only divided into three regions per state and input instantiation, making the point location problem very efficient. Moreover, given the locality constraints, the subproblems are of much smaller dimension than the full problem, which consequently significantly reduces the computational overhead of explicit solutions. We conclude with numerical simulations to demonstrate the computational advantages of our method, in which we show a large improvement in runtime per MPC iteration as compared with the results of computing the optimization with a solver online.

Keywords: Distributed control, Predictive control for linear systems, Agents-based systems
Abstract: This paper revisits the theory and motivation of external soft constraints to encounter feasibility problems in non-iterative distributed model predictive control that are due to prediction mismatch. Using the idea of exact penalty theory for centralized model predictive control as a starting point, an approach is developed that ensures collision-freeness between a group of homogeneous agents in an environment with obstacles, based on recursive feasibility and a conditional hard constraint. Simulation results that illustrate the approach are presented and discussed.

Keywords: Distributed control, Optimization algorithms, Time-varying systems
Abstract: This paper is devoted to the distributed continuous-time optimization problem with time-varying objective functions and time-varying nonlinear inequality constraints. Different from most studied distributed optimization problems with time-invariant objective functions and constraints, the optimal solution in this paper is time varying and forms a trajectory. To minimize the global time-varying objective function subject to time-varying local constraint functions using only local information and local interaction, we present a distributed control algorithm that consists of a sliding-mode part and a Hessian-based optimization part. The asymptotical convergence of the proposed algorithm to the optimal solution is studied under suitable assumptions. The effectiveness of the proposed scheme is demonstrated through a simulation example.

Keywords: Distributed control, Large-scale systems, Networked control systems
Abstract: This paper proposes a novel method for distributed controller synthesis of homogeneous interconnected systems consisting of identical subsystems. The objective of the designed controller is to minimize the L2 gain of the performance channel. The proposed method is an extended formulation of the Full Block S-Procedure (FBSP) where we introduce an additional set of variables. This allows to relax the block-diagonal structural assumptions on the Lyapunov and multiplier matrices required for distributed control design, which reduces conservatism w.r.t. most existing approaches. We show how to decompose the proposed extended FBSP into small synthesis conditions in the size of one individual subsystem.

Keywords: Distributed control, Stability of nonlinear systems, Stability of linear systems
Abstract: In this paper, we discuss our recent works on the null-controllability, the exact controllability, and the stabilization of linear hyperbolic systems in one dimensional space using boundary controls on one side for the optimal time. Under precise and generic assumptions on the boundary conditions on the other side, we first obtain the optimal time for the null and the exact controllability for these systems for a generic source term. We then prove the null-controllability and the exact controllability for any time greater than the optimal time and for any source term. Finally, for homogeneous systems, we design feedbacks which stabilize the systems and bring them to the zero state at the optimal time. Extensions for the non-linear homogeneous system are also discussed.

Keywords: Distributed control, Optimal control, Distributed parameter systems
Abstract: Controlling a population of dynamic systems has been of great interest and importance in recent years due to its broad impact on diverse real-life applications, including nuclear magnetic resonance (NMR) in quantum physics, disease treatment in bio-medicine, and spiking patterns in neuroscience. Although optimal control of a single or multiple dynamic system has been a well-studied subject in both applied mathematics and systems engineering, effective methods for solving emerging optimal control problems involving a large population of nonlinear dynamic systems are underdeveloped.These burgeoning problems require robust control over the evolution of the entire population of dynamic systems, or at least, in the distributional sense. It is more challenging with the consideration of the control design involving nonlinear dynamics which has a very strong localized structure, i.e., every single sub-system follows a structurally identical dynamic. In this work, we first explore the dynamic model of a population system with Liouville equation that describes the evolution of the system population. Then, extending our previous work, we generate a robust numerical method, the iterative method, to find the desired optimal controls with both free- and fixed-endpoint conditions. Several practical examples are included in this paper to discuss the advantages and limitations of this iterative method.

Keywords: Distributed control, Cooperative control, Machine learning
Abstract: In this work we will provide a finite-sample analysis of a distributed gradient temporal difference algorithm for policy evaluation with value functions that lie in Reproducing Kernel Hilbert Spaces(RKHS). This work focuses on multi-agent systems where each agent observes a private reward and agents can only communicate with nearby neighbors under time varying networks. The main result is a time-evolving upper bound of the second order error statistics of the algorithm, which accounts for the evolution of the consensus error as well as the average approximation error.This result shows that the distributed learning algorithm under consideration can achieve a bounded final error covariance that is inversely proportional to the algorithm step-size, which is consistent with results in the more general field of stochastic approximation.

Keywords: Distributed parameter systems, Optimal control, Computational methods
Abstract: In 1961 E. G. Albrekht presented a method for the optimal stabilization of smooth, nonlinear, finite dimensional, continuous time control systems. This method has been extended to similar systems in discrete time and to some stochastic systems in continuous and discrete time. In this paper we extend Albrekht's method to the optimal stabilization of some smooth, nonlinear, infinite dimensional, continuous time control systems whose nonlinearities are described by Fredholm integral operators.

Keywords: Traffic control, Distributed parameter systems, Switched systems
Abstract: This paper investigates deterministic and stochastic stability of mixed-autonomy traffic with connected and autonomous vehicle (CAV) platoons and conventional vehicles on a freeway segment. The deterministic traffic dynamics is described with a two-class Aw-Rascle (AR) traffic partial differential equations (PDEs) model. PDE states describe the evolution of densities and velocities of two-class vehicles on freeway over time and space. We consider that one class represents the human-driven vehicles while the other class represents the CAV platoon with bigger size but slower speed. We linearize the 4 times 4 hyperbolic PDE model around spatially uniform steady states which gives four characteristic speeds positive in the free traffic with one negative characteristic appearing in the congested traffic. The upstream propagation of velocity perturbation information potentially destroys the traffic stability. Trade-offs between stability and maximum flow rate are discussed for different ratios of CAV platoons in the mixed traffic. The uncertainty is then introduced to capture the randomness in the arrival rate of incoming CAV traffic. We focus on a simple two-mode continuous-time Markov process taking values from a set of two operation modes that represent the qualitatively distinct traffic dynamics (congestion versus free flow). Therefore, a linear hyperbolic PDEs with Markov jump model parameters and boundary conditions is considered, consisting of both the continuous PDE states and the discrete operational mode. The stochastic stability is then analyzed using the Lyapunov approach. The sufficient conditions for stochastically?exponential stability are derived for the Markov switching system. Some implications for CAV platooning operations to limit the negative effect of the randomness are also discussed.

Keywords: Distributed parameter systems, Traffic control, LMIs
Abstract: Traffic control of congestion regimes is considered in this paper. A perturbed distributed parameter model is used, and a boundary control is designed to reject the perturbations. More precisely an optimal proportional-integral (PI) feedback control law is computed to maximally reject the disturbances, and to stabilize the traffic in congested regime. The disturbance applies at the boundary of the linearized Aw-Rascle-Zhang (ARZ) model. Therefore the disturbance operator is unbounded, rendering the control problem very challenging. In order to analyze and design the optimal PI controller for this infinite-dimensional system, the L2 gain is computed to estimate the disturbance rejection. Numerically tractable conditions are computed and written with linear matrix inequalities (LMIs). As a result, the estimation of an upper bound of the L2 gain, from the disturbance to the controlled output, can be formulated as an optimization problem with LMI constraints. The validity of this method is checked on simulations of the nonlinear ARZ model in closed-loop with this optimal PI controller.

Keywords: Model/Controller reduction, Nonlinear systems identification, Fluid flow systems
Abstract: Isostable reduction is a powerful technique for characterizing the transient behavior of a weakly forced, nonlinear dynamical systems in relation to a stable attractor. Practically, this reduction strategy requires small magnitude inputs so that the state remains close to the underlying attractor; when inputs become too large the reduction becomes unusable. Here, we develop an adaptive isostable coordinate framework that is valid for a continuous family of system parameters. Relations are derived that capture changes to the isostable coordinates in response to parameter changes. This information is subsequently used to define a reduction strategy valid for large magnitude but slowly varying inputs. The proposed reduction framework is compared to well-established linear and nonlinear proper orthogonal decomposition (POD) reduction techniques for simulations of the 1-dimensional nonlinear Burgers' equation with time-varying Dirichlet boundary conditions. In numerical simulations the proposed reduction strategy only requires a single mode to accurately capture system behavior. By contrast, the linear POD reduction performs poorly while the nonlinear POD strategy requires several modes to achieve comparable performance.

Keywords: Distributed parameter systems, Agents-based systems
Abstract: A network of agents, modeled by a class of wave PDEs, is under investigation. One agent in the network plays the role of a leader, and all the remaining ?follower? agents are required to asymptotically track the state of the leader. Only boundary sensing of the agent?s state is assumed, and each agent is controlled through the boundary by Neumann-type actuation. A linear interaction protocol is proposed and analyzed by means of a Lyapunov-based approach. A simple set of tuning rules, guaranteeing the exponential achievement of synchronization, is obtained. In addition, an exponential ISS relation, characterizing the effects on the tracking accuracy of boundary and in-domain disturbances, is derived for the closed loop system.

Keywords: Sampled-data control, Networked control systems, Delay systems
Abstract: This paper, for the first time, provides sub-predictors for networked control systems under uncertain large communication delays. We use a time-delay approach to NCS and employ sub-predictors to partially compensate large uncertain transmission delays in the sensor-to-controller and controller-to-actuator channels by dividing the long delay into small pieces. We consider systems with norm-bounded uncertainties, and take into account Round-Robin scheduling protocol in sensor-to-controller channel. In comparison with the traditional reduction-based classical predictor involving distributed input, the sub-predictor-based feedback is more friendly in the presence of norm-bounded uncertainties and is simpler for implementation. The stability analysis of the closed-loop system is based on the Lyapunov-Krasovskii method and the stability conditions are given in terms of linear matrix inequality.

Keywords: Distributed parameter systems, Optimal control, Lyapunov methods
Abstract: In this paper, we present a convex formulation of {H}_{infty}-optimal control problem for coupled linear ODE-PDE systems with one spatial dimension. First, we reformulate the coupled ODE-PDE system as a Partial Integral Equation (PIE) system and show that stability and {H}_{infty} performance of the PIE system implies that of the ODE-PDE system. We then construct a dual PIE system and show that asymptotic stability and {H}_{infty} performance of the dual system is equivalent to that of the primal PIE system. Next, we pose a convex dual formulation of the stability and {H}_{infty}-performance problems using the Linear PI Inequality (LPI) framework. LPIs are a generalization of LMIs to Partial Integral (PI) operators and can be solved using PIETOOLS, a MATLAB toolbox. Next, we use our duality results to formulate the stabilization and {H}_{infty}-optimal state-feedback control problems as LPIs. Finally, we illustrate the accuracy and scalability of the algorithms by constructing controllers for several numerical examples.

Keywords: Uncertain systems, Sampled-data control, Switched systems
Abstract: In robotic systems, perception latency is a term that refers to the computing time, measured from the data acquisition to the moment in which perception output is ready to be used to compute control commands. There is a clear compromise between perception latency and the stability of the overall robotic system, referred here as the latency-precision trade-off. Opposed to periodic sampling, which forces a particular perception latency, we study for the first time the computation of the best sequence of latencies, obtaining different precision at different moments in time. Using this concept we give a formal problem formulation of the attention-precision trade-off. Moreover, we give a method to obtain sequences of latencies that improve the system performance which is verified by simulation experiments.

Keywords: Resilient Control Systems, Optimal control, Robust control
Abstract: In optimal control problems, disturbances are typically dealt with using robust solutions, such as H-infinity or tube model predictive control, that plan control actions feasible for the worst-case disturbance. Yet, planning for every contingency can lead to over-conservative, poorly performing solutions or even, in extreme cases, to infeasibility. Resilience addresses these shortcomings by adapting the underlying control problem, e.g., by relaxing its specifications, to obtain a feasible, possibly still valuable trajectory. Despite their different aspects, robustness and resilience are often conflated in the context of dynamical systems and control. The goal of this paper is to formalize, in the context of optimal control, the concept of resilience understood as above, i.e., in terms of adaptation. To do so, we introduce a resilient formulation of optimal control by allowing disruption-dependent modifications of the requirements that induce the desired resilient behavior. We then propose a framework to design these behaviors automatically by trading off control performance and requirement violations. We analyze this resilience-by-compromise method to obtain inverse optimality results and quantify the effect of disturbances on the induced requirement relaxations. By proving that robustness and resilience optimize different objectives, we show that these are in fact distinct system properties. We conclude by illustrating the effect of resilience in different control problems.

Keywords: Resilient Control Systems, Agents-based systems, Networked control systems
Abstract: In this paper, we investigate the problem of rendezvous of second-order agents considering two issues: a) misbehaving agents that make update abnormally and can send arbitrary information to neighbors; b) unknown but bounded communication noise. Both issues can deteriorate the rendezvous performance and even destabilize the systems. We propose a self-triggered resilient rendezvous algorithm, which guarantees that the operation of normal agents is unaffected by the disruption of misbehaving agents and ensures practical rendezvous of normal agents. The position and velocity of normal agents always evolve boundedly, and the agent-to-agent position error converges to be bounded by a value scaling with the magnitude of communication noise. By the proposed algorithm, each agent can sample its neighbors and update its control sporadically and fully asynchronously

Keywords: Resilient Control Systems, Networked control systems, Control over communications
Abstract: State-dependent attack and defense mechanisms in a wireless networked control system are investigated. The controller in this system attempts to transmit control commands to a remotely located plant by using a wireless channel that is subject to jamming attacks from an adversary. The probability of a failure on this channel depends on the powers of both the transmission signal emitted from the controller and the jamming interference signal emitted from the attacker. We show that if the power levels of transmissions from the controller are consistently above a threshold and the average power level of the jamming interference is sufficiently small, then the networked control system is guaranteed to be almost surely asymptotically stable. However, it is hard to analytically derive optimal attack and defense policies due to the complexity of the wireless channel model. To find out potentially dangerous attacks and high-performance defense policies, we propose a search-based approach and utilize genetic algorithms. Specifically, by considering Voronoi partitions of the state space, we find attack policies that achieve large quadratic costs. We use the search-based approach also for designing defense policies, where the controller adjusts the power of the transmission signal based on the plant's state information. The efficacy of the proposed approach is demonstrated through a number of simulation-based experiments.

Keywords: Resilient Control Systems, Optimization algorithms, Smart grid
Abstract: This paper mainly studied the distributed economic dispatch optimization problem of power system which takes the security of communication network into consideration. Firstly, a new single area power system economic dispatch model is given which takes the environmental pollution penalty into account. An optimization approach based on gradient descent and multi-agent consensus protocol is proposed to solve the generation cost minimization problem. A novel distributed resilient event-triggered scheme is proposed to ensure the stability and economy of power system under denial of service (DoS) attack. Then the prerequisites to minimize the system power generation cost are analyzed from the aspects of optimality and economy. Finally, the effectiveness of the proposed method is verified by simulation experiments.

Keywords: Resilient Control Systems, Cyber-Physical Security, Distributed control
Abstract: The problem of mitigating maliciously injected signals in interconnected systems is dealt with in this paper. We consider the class of covert attacks, as they are stealthy and cannot be detected by conventional means in centralized settings. Distributed architectures can be leveraged for revealing these stealthy attacks by exploiting communication and local model knowledge. We show how such detection schemes can be improved to estimate the action of an attacker and we propose an accommodation scheme in order to mitigate or neutralize abnormal behavior of a system under attack.

Keywords: Communication networks, Fault tolerant systems, Sensor networks
Abstract: In Wireless Sensor Networks (WSNs), equally spaced timing for Medium Access Control (MAC) is fundamental to guarantee throughput maximization from all nodes. This motivated the so called desynchronization problem and its solution based on the fast Nesterov method. In this paper, we tackle the problem of constructing centralized and distributed versions of the optimal fixed-parameter Nesterov that are resilient to attacks to a subset of nodes. By showing a relationship between the variance of the attacker signal and how further away a node is, we are able to present a distributed algorithm that has minimal added complexity and performs the detection and isolation of the faulty node. Simulations are provided illustrating the successful detection and highlighting that without a correction mechanism (dependent on additional assumptions), there is a residual error that is not eliminated.

Keywords: Observers for nonlinear systems, Resilient Control Systems, Smart grid
Abstract: The state estimation of continuous-time nonlinear systems in which a subset of sensor outputs can be maliciously controlled through injecting a potentially unbounded additive signal is considered in this paper. Analogous to our earlier work for continuous-time linear systems in cite{chong2015observability}, we term the convergence of the estimates to the true states in the presence of sensor attacks as `observability under M attacks', where M refers to the number of sensors which the attacker has access to. Unlike the linear case, we only provide a sufficient condition such that a nonlinear system is observable under M attacks. The condition requires the existence of asymptotic observers which are robust with respect to the attack signals in an input-to-state stable sense. We show that an algorithm to choose a compatible state estimate from the state estimates generated by a bank of observers achieves asymptotic state reconstruction. We also provide a constructive method for a class of nonlinear systems to design state observers which have the desirable robustness property. The relevance of this study is illustrated on monitoring the safe operation of a power distribution network.

Keywords: Stability of nonlinear systems, Stability of hybrid systems, Time-varying systems
Abstract: Very recently, it has been shown that the standard notion of stability for impulsive systems, whereby the state is ensured to approach the equilibrium only as continuous time elapses, is too weak to allow for any meaningful type of robustness in a time-varying impulsive system setting. By strengthening the notion of stability so that convergence to the equilibrium occurs not only as time elapses but also as the number of jumps increases, some facts that are well-established for time-invariant nonimpulsive systems can be recovered for impulsive systems. In this context, our contribution is to provide novel results consisting in rather mild conditions under which stability under zero input implies stability under inputs that converge to zero in some appropriate sense.

Keywords: Hybrid systems, Constrained control, Optimal control
Abstract: Nominally well-posed hybrid inclusions are a class of hybrid dynamical systems characterized by outer/upper semicontinuous dependence of solutions on initial conditions. In the context of reachable sets of hybrid systems, this property guarantees outer/upper semicontinuous dependence with respect to both initial conditions and time. This article defines a counterpart to the notion of nominal well-posedness, referred to as nominal inner well-posedness, which ensures inner/lower semicontinuous dependence of solutions on initial conditions. Consequently, it is shown that reachable sets of nominally inner well-posed hybrid systems depend inner/lower semicontinuously on initial conditions and time under appropriate assumptions. Sufficient conditions guaranteeing nominal inner well-posedness are provided and demonstrated with an example.

Keywords: Hybrid systems, Estimation, Sensor networks
Abstract: This paper studies the problem of distributed state estimation for stochastic linear hybrid systems. Building on the centralized interacting multiple model algorithm, a novel distributed state estimation technique is proposed. In our distributed setting, a network of sensors is employed and each sensor measures only a portion of the system outputs. It should be noted that the system might not be observable for each individual sensor. In this paper, we aim to develop an effective scheme that enables the sensor network to collectively estimate the hybrid system states (both the continuous states and discrete modes), by leveraging the cooperation among multiple sensors. Consequently, each sensor only needs to process a relatively small set of data and will be able to locally and identically observe the states of stochastic linear hybrid systems. The validation and performance of the proposed scheme are demonstrated by numerical simulations on an aircraft tracking problem finally.

Keywords: Hybrid systems, Observers for nonlinear systems, Estimation
Abstract: Notions of observer and detectability are well established for continuous-time (CT) and discrete-time (DT) systems, and are known to be linked, since a system must be detectable to admit an observer. Unfortunately, defining such notions for a hybrid system is not straightforward because solutions do not share the same hybrid time domain. In this paper, we propose to define observers and detectability for hybrid systems, such that detectability is still necessary for the existence of an observer and such that standard definitions are recovered for CT and DT systems, when seen as special cases of hybrid systems. We rely on a recent definition of hybrid systems with hybrid inputs and use jump reparametrizations to define convergence and equality of outputs.

Keywords: Hybrid systems, Quantized systems, Supervisory control
Abstract: systematic framework to address control design of several classes of hybrid systems with sophisticated control objectives. However, results available in the literature are not concerned with impulsive systems which are an important modeling framework of many applications. In this paper, we provide an approach for constructing symbolic models for a class of impulsive systems possessing some stability properties. We formally relate impulsive systems and their symbolic models using a notion of so-called alternating simulation function. We show that behaviors of the constructed symbolic models are approximately equivalent to those of the impulsive systems. Finally, we illustrate the effectiveness of our results through a case study.

Keywords: Switched systems, Hybrid systems, Control applications
Abstract: This paper shows that for a single-input single-output linear time-invariant plant having a real unstable open-loop pole, the overshoot inherent when using any stabilizing linear time-invariant feedback controller can be eliminated with a hybrid integrator-gain-based control strategy. Key design considerations underlying the presented controller are discussed, and an interpretation of the working mechanism is provided.

Keywords: Stability of nonlinear systems, Stability of hybrid systems
Abstract: Nowadays, the demand for an alternative to linear PID controllers has increased because of the rising expectations of the high-precision industry. The potential of reset controllers to solve this important challenge has been extensively demon- strated in the literature. However, similarly to other non-linear controllers, the stability analysis for these controllers is complex and relies on parametric models of the systems which may hinder the applicability of these controllers in industry. The well-known Hβ method tries to solve this significant issue. However, assessing the Hβ condition in the frequency-domain is complex, especially for high dimensional plants. In addition, it cannot be used to assess UBIBS stability of reset control systems in the case of reseting to non-zero values. These problems have been solved in this paper for the first order reset elements, and an easy-to-use frequency approach for assessing stability of reset control systems is proposed. The effectiveness of the proposed approach is demonstrated through a practical example.

Keywords: Stability of hybrid systems, Stability of nonlinear systems, Simulation
Abstract: In this paper, we analyse the impact of delayed event detection on the stability of a 2-mode planar hybrid automata. We consider hybrid automata with a unique equilibrium point for all the modes, and we find the maximum delay that preserves stability of that equilibrium point. We also show for the class of hybrid automata treated that the instability of the equilibrium point for the equivalent hybrid automaton with delay in the transitions is equivalent to the existence of a closed orbit in the hybrid state space, a result that is inspired by the Joint Spectral Radius theorem. This leads to an algorithm for computing the maximum stable delay exactly. Other potential applications of our technique include co-simulation, networked control systems and delayed controlled switching with a state feedback control.

Keywords: Agents-based systems, Cooperative control, Decentralized control
Abstract: Synchronization on the sphere is important to certain control applications in swarm robotics. Of recent interest is the Lohe model, which generalizes the Kuramoto model from the circle to the sphere. The Lohe model is mainly studied in mathematical physics as a toy model of quantum synchronization. The model makes few assumptions, wherefore it is well-suited to represent a swarm. Previous work on this model has focused on the cases of complete and acyclic networks or the homogeneous case where all oscillator frequencies are equal. This paper concerns the case of heterogeneous oscillators connected by a non-trivial network. We show that any undesired equilibrium is exponentially unstable if the frequencies satisfy a given bound. This property can also be interpreted as a robustness result for small model perturbations of the homogeneous case with zero frequencies. As such, the Lohe model is a good choice for control applications in swarm robotics.

Keywords: Control over communications, Cooperative control, Uncertain systems
Abstract: In this paper, we consider the synchronization of two linear systems that are subject to unknown perturbations. One of the systems is driven by a reference signal, which is unknown to the second system. Both systems can only use a one-way communication channel to exchange information. The channel is subject to data-rate constraints. The messages are generated by a smart sensor that measures the state and is capable of performing some computations. The messages are received by a controller which interprets them to apply an appropriate control input to the system. The objective is to design a sensor/controller pair, which we will refer to as a communication protocol, such that the distance between the states of both systems is bounded, and as small as possible communication rate is necessary. In this paper, a communication protocol that achieves this objective is presented together with the minimum channel rate to implement it. Simulations of the communication protocol are provided to support the theoretical work.

Keywords: Cooperative control, Control of networks, Constrained control
Abstract: In this paper, the bearing-only formation tracking control problem of multi-agent systems modeled as double-integrators in local reference frames is investigated. The sensing topology among all agents is described by a multiply rooted undirected graph and the autonomous leaders associated with a common reference frame move with a constant velocity. The proposed control law for each follower depends merely on the relative bearings and relative orientations to its neighbors in its local reference frame. The orientation synchronization problem is first solved so that all orientations of the followers converge to that of the leaders. Then, a bearing-only controller is developed to achieve the desired moving formation. Finally, an example illustrates the effectiveness.

Keywords: Adaptive control, Adaptive systems, Direct adaptive control
Abstract: This work proposes a distributed composite adaptive synchronization algorithm for multiple uncertain Euler-Lagrange (EL) systems, where parameter convergence is achieved under a relaxed mathematical condition as compared to the state-of-the-art. Classical adaptive controllers require an analytical condition, called persistence of excitation (PE), to ensure parameter convergence, which results in better transient performance and robustness to disturbance. The PE condition is extended to Cooperative-PE (C-PE) condition for distributed adaptive controllers with cooperative estimation strategies. The PE and C-PE conditions are restrictive in nature since these conditions are not satisfied in most practical applications. Recent literature in adaptive control has relaxed the PE condition to Initial Excitation (IE), which is shown to be sufficient for parameter convergence. The IE condition is argued to be significantly milder than PE and can be satisfied in many practical settings. The proposed result further extends the IE condition to Cooperative-IE (C-IE) condition in distributed adaptive control architecture in the context of synchronizing multiple EL systems. It is established that the C-IE condition is milder than IE and C-PE conditions. Two-tier filter based estimation algorithm with strategic switching ensures parameter convergence under the C-IE condition and thereby provides exponential convergence of tracking and parameter estimation error to zero. Simulation results validate the efficacy of the proposed algorithm is compared to conventional distributed adaptive controllers in terms of superior tracking and estimation performance.

Keywords: Linear systems, Switched systems, Networked control systems
Abstract: In this work, we propose an emergent dynamics based tool to approximate the synchronizing behavior in large networks of interconnected systems/agents. Unlike the existing results considering fixed or smoothly varying topologies, we study the case in which the interactions are suddenly (de)activated generating switchings in the interconnection topology. We assume that the state of all agents is of the same dimension but their linear dynamics is defined by different state matrices. The coupling between agents is done through a decentralized state-feedback law and the goal of this paper is to show that, the synchronizing behavior of the agents can be approximated by a switching emerging dynamics that is independent of the control gain (when this gain is large enough). The results require the boundedness of the trajectory of the switching emergent dynamics which is ensured under mild assumptions by introducing a minimum dwell-time between two consecutive interconnection topology switchings. Numerical simulations illustrate the theoretical results.

Keywords: Network analysis and control, Linear systems, Distributed parameter systems
Abstract: It is known that synchronization of (identical) coupled finite-dimensional linear systems is characterized by the spectrum of the Laplacian matrix and stability properties of the isolated systems. This characterization, in general, fails for infinite-dimensional linear systems. This paper identifies a class of systems for which this characterization remains valid. As an illustration, the theoretical results are used to study synchronization of coupled heat equations.

Keywords: Network analysis and control, Stability of nonlinear systems
Abstract: This paper presents synchronization conditions for a third-order Kuramoto network, which is inspired by a transient model of the electric power network. In this model, the amplitude dynamics of oscillators are introduced into a conventional second-order Kuramoto network. By using an energy function method, we propose sufficient conditions on the initial configurations of a Kuramoto network to determine the stability of phases and amplitudes of oscillators. Then, we show that these conditions ensure the synchronization in frequencies and phases of oscillators. Furthermore, an algorithm is designed to calculate an ultimate bound for the phase differences of oscillators at synchronized state, which evaluates overall network synchronization performance.

Keywords: Network analysis and control, Stability of nonlinear systems, Optimization algorithms
Abstract: Synchronization is an essential property of engineered and natural networked dynamical systems. The Kuramoto model of nonlinear synchronization has been widely studied in applications including entrainment of clock cells in brain networks and power system stability. Synchronization of Kuramoto networks has been found to be challenging in the presence of signed couplings between oscillators and when the network includes oscillators with heterogeneous natural frequencies. In this paper, we study the problem of minimum-set control input selection for synchronizing signed Kuramoto networks. We first derive sufficient conditions for synchronization in homogeneous as well as heterogeneous Kuramoto networks using a passivity-based framework. We then develop a submodular algorithm for selecting a minimum set of control inputs for a given Kuramoto network. We evaluate our approach through a numerical study on multiple classes of graphs, including undirected, directed, and cycle graphs.

Keywords: Game theory, Network analysis and control, Decentralized control
Abstract: In this talk, we consider decentralized (game-theoretic) vaccination decisions by humans during susceptible-infected-susceptible epidemics on networks. We consider a population game framework where nodes choose whether or not to vaccinate themselves, and the epidemic risk is defined as the infection probability at the endemic state of the epidemic. We examine the impacts of behavioral biases and nonlinear probability weighting by human decision-makers on the Nash equilibrium protection strategies. In particular, we characterize the effects of over- and under-estimation of infection probabilities on the vaccination decisions by the individuals in the network. We first establish the existence and uniqueness of a threshold equilibrium where nodes with degrees larger than a certain threshold vaccinate. When the perceived vaccination cost is sufficiently high, we show that behavioral biases cause fewer players to vaccinate, and vice versa. We quantify this effect for a class of networks with power-law degree distributions by proving tight bounds on the ratio of equilibrium thresholds under behavioral and true perceptions of probabilities. We further characterize the socially optimal vaccination policy and investigate the inefficiency of the Nash equilibrium. In particular, we show that reducing the perceived cost of vaccination (e.g., via subsidies, etc.) can compensate for behavioral biases and lead the individuals to make socially optimal decisions.

Keywords: Network analysis and control, Large-scale systems, Networked control systems
Abstract: Scalability problems often arise when studying disease propagation on interaction networks within a community. This problem is further compounded as the scope of the modelling increases to city-wide and multi-city interactions. One approach is to treat each node in the network as a collection of individuals, where the assumption of well-mixing is assumed to be reasonable. This talk will address a distinctive set of reduction techniques that leverages the inherent geographic and functional network-of-networks structures that appears within the network. Geographical layering, such as in multi-city epidemics models, promotes the use of natural time-scale differences in the system. The dynamics can then be individually studied under a separation principle, simplifying analysis. Functional layering, into population types, can be modelled using graph products that factor the network dynamics while preserving the distinctive features of the network structure. Theory relating to network-of-networks with multiple time-scales and Cartesian graph products will be explored with quantitative bounds on the reduced-order models, computationally efficient disease trajectory calculations and analysis of convergence to disease-free state, and the design of distributed controllers. These scalable techniques on large-scale network can provide efficient modelling, performant vaccination strategies, and distributed infection management systems.

Keywords: Biological systems, Biomolecular systems, Biotechnology
Abstract: More than 150 COVID-19 vaccine candidates were under development in June 2020, of which a much smaller subset will be safe and provide lasting immunity. Multiple vaccine candidates were found to be safe and then entered phase III human trials in Summer 2020 to test their effectiveness in providing some protection against the disease.

A vaccine will not be available to the public by then, however. The discovery of a COVID-19 vaccine that is effective in humans is not the same thing as making that vaccine available to the world. Many time-consuming engineering tasks are involved in going from the biology of creating a COVID-19 vaccine to the vaccination of billions of individuals needed to protect the world population. A major bottleneck to world-scale vaccination is the time required to develop a process to manufacture billions of doses within the existing supply chains and equipment while maintaining the highest levels of safety in the product.

After a brief summary of the most promising COVID-19 vaccines and the bottlenecks in vaccine manufacturing in general, ways are described for using feedback control to shorten the timeline. The first set of technologies are applicable to all vaccine types and involve the use of fully automated modular manufacturing systems. Control theory and algorithms are described for addressing the characteristics of these highly uncertain, nonlinear, hybrid, distributed parameter systems. The second set of technologies is specific to the main class of vaccines, live-attenuated viral vaccines, which use a weakened form of the virus. The close similarity of the vaccines to the natural infection creates a strong and long-lasting immune response. Such vaccines include influenza (flu), measles, mumps, rubella, rotavirus, smallpox, chickenpox, and yellow fever. In a case study, feedback control enables more than a factor of five increase in vaccine production.

Keywords: Healthcare and medical systems, Biotechnology, Control of networks
Abstract: Panel Discussion: How do we prepare for the future vaccine now?

Moderators: Fabrizio Dabbene and Maria Elena Valcher Panelists: Sarah Spurgeon, Shreyas Sundaram, Masaki Ogura

The ongoing pandemic has stimulated an impressive race all around the world to develop a vaccine against Covid-19. As of September 4, more than 170 candidate vaccines are currently tracked by the World Health Organization (WHO).

The standard procedures for testing vaccines typically take years, a significantly long period of time necessary to ensure the highest safety standards, in fact higher than for other drugs, because they are given to millions of healthy people.

Indeed, typical testing involves several steps:

- Pre-clinical stage: researchers give administer the vaccine to animals to see if it triggers an immune response.

- Phase 1: the vaccine is given to a small group of people to determine whether it is safe and to learn more about the immune response it provokes.

- Phase 2: the vaccine is given to hundreds of people so scientists can learn more about its safety and correct dosage.

- Phase 3: the vaccine is given to thousands of people to confirm its safety ? including rare side effects ? and effectiveness. These trials involve a control group which is given a placebo.

The emergency has pushed for a rapid response and scientists are hoping to develop a vaccine for Covid-19 within 12 to 18 months.

After these phases, a massive vaccine production will be necessary. This will represent a focal challenge for the pharmaceutical industry.

Several natural questions arise:

- How should we behave while waiting for the vaccine to be available?

- How long will it take before the vaccine is available?

- What are the potential risks of the vaccine, in light of such a short testing period?

- What about liability?

- Should vaccination be compulsory to ensure herd immunity?

- How should we cope with possible resistance to mass vaccination (e.g. anti-vax movements)?

- Will the vaccine be accessible to everybody or there will be a "vaccine sovereignity"?

- How can we help? Can our models forecast the effects of vaccination in a reliable way and influence political decisions? How control can be instrumental in speeding the vaccine manufacturing process?

Keywords: Systems biology, Biomolecular systems, Biological systems
Abstract: We describe a multicellular approach to control a target cell population endowed with a bistable toggle-switch. The idea is to engineer a synthetic microbial consortium consisting of three different cell populations. In such a consortium, two populations, the Togglers, responding to some reference input, can induce the switch of a bistable memory mechanism in a third population, the Targets, so as to activate or deactivate some additional functionalities in the cells. Communication among the three populations is established by orthogonal quorum sensing molecules that are used to close a feedback control loop across the populations. The control design is validated via in-silico experiments in BSim, a realistic agent-based simulator of bacterial populations.

Keywords: Biological systems, Stochastic systems, Modeling
Abstract: The dynamics of the size distribution in growing and dividing rod-shaped bacteria can change depending on the perspective through which the cell population is observed. From the perspective of single-cell lineages, only one descendant is followed after each division, while in population snapshots all of the offspring is considered. In this work, we propose an analytical derivation of Population Balance Equations (PBEs) that can be used to compute the dynamics of the main statistics of the cell size distribution. We then explore how the dynamics are affected by different division strategies and by the two different perspectives of observation. To assess the accuracy of our derivations, we compare the analytical results with those obtained numerically and through stochastic simulations. The comparison allows us to establish mathematical relationships between the two perspectives of observation, thus improving our knowledge of how cells control their growth and proliferation.

Keywords: Uncertain systems, Systems biology
Abstract: In systems biology, perfect adaptation (adaptation) denotes the property of a system reacting to a step input stimulus by completely (partially) restoring the pre-stimulus output value at steady state. We address the problem of predicting adaptation for uncertain dynamical systems. To this aim, we introduce a formal definition of adaptation tailored to the robust analysis of dynamical systems. Whilst the definition is more general and valid also for the step response analysis of nonlinear systems, in the linear case such a definition of adaptation reduces to the presence of a single real zero that dominates all poles. Based on this definition, we can assess robust adaptation by means of the robust real plot, which characterises the position of real zeros and poles for linear systems with parametric uncertainties.

Keywords: Genetic regulatory systems, Biological systems, Cellular dynamics
Abstract: Gene expression is inherently a stochastic process, leading to randomness in the timing of events. A problem of interest is to understand how cells achieve temporal precision. Previous work has shown that if a gene product (protein) is stable then a no feedback strategy provides minimum noise in timing. Here we investigate the form of optimal feedback strategy when the protein production rate is affected by an external dynamic disturbance (noise). We specifically consider a telegraph process (two state) for the external disturbance and show that the best strategy is still no feedback. Using this strategy, we provide an exact formula for the minimum achievable noise. Finally, we examine the effect of model parameters on the minimum noise.

Keywords: Biomolecular systems, Cellular dynamics
Abstract: Genetically-identical cells can show remarkable intercellular variability in the level of a given protein which is commonly known as the gene expression noise. Besides intrinsic fluctuations that arise from the inherent stochasticity of the biochemical processes, a significant source of expression noise is extrinsic. Such extrinsic noise in gene expression arises from cell-to-cell differences in expression machinery, transcription factors, cell size, and cell cycle stage. Here, we consider the synthesis of a transcription factor (TF) whose production is impacted by a dynamic extrinsic disturbance, and systematically investigate the regulation of expression noise by decoy sites that can sequester the TF. Our analysis shows that increasing decoy numbers reduce noise in the level of the free (unbound) TF with noise levels approaching the Poisson limit for large number of decoys. Interestingly, the suppression of expression noise compared to no-decoy levels is maximized at intermediate disturbance timescales. Finally, we quantify the noise propagation from the TF to a downstream target protein and find counterintuitive behaviors. More specifically, for nonlinear dose responses of target-protein activation, the noise in the target protein can increase with the inclusion of decoys, and this phenomenon is explained by smaller but more prolonged fluctuations in the TF level. In summary, our results illustrates the nontrivial effects of high-affinity decoys in shaping the stochastic dynamics of gene expression to alter cell fate and phenotype at the single-cell level.

Keywords: PID control, Flight control, Control applications
Abstract: This paper presents a guide for designing a set of PID or first-order type attitude controllers for a bank of F-16 longitudinal dynamic models, so that any one of the controller set satisfies the prescribed handling quality requirements. For a scaled down F-16 aircraft, the longitudinal dynamic models between elevator and pitch angle have been identified using the weighted moment matching method with wind tunnel tests, in which ten experiments were performed at three wind velocities, 15 ~m/s, 20 ~m/s, and 25 ~m/s, as the trimmed conditions. The average transfer function models at these trimmed points constitute the model bank M. We here consider the gain and phase margins, the maximum overshoot and settling time limits as the handling quality requirements. In the proposed approach, we first use modern analytical PID design methods to find the entire set of PI (or first-order) controllers that guarantee the stability margin for a given plant model. Then from this set, we obtain the controller set that satisfies the time response requirements. Repeating this process for three models and taking the intersection of each controller set, we obtain a controller set C that simultaneously meets the prescribed specifications. This set is shown in a 3-D graphic. Simulation shows that any controller selected in this set C meets the design objectives in all three models.

Keywords: Emerging control applications, PID control, Computer-aided control design
Abstract: Stabilizing gimbals are ubiquitous within the unmanned aerial and ground system robotics communities as they permit acquisition of a variety of sensing modalities, typically vision, while removing undesired rapid orientation changes that a vehicle might experience. In this paper, we leverage a commercial gimbal controller to construct a highly reconfigurable rapid prototyped gimbal setup and compute a practical set of stabilizing PID controllers for the gimbal. The novelty in this research is that the method constructively determines the set of stabilizing PID controllers using only direct data measurement without additional knowledge such as the identification of the plant model, order of the system and number of poles and zeros. The set guarantees stability and, thus, is particular to each plant to be controlled. This feature is an attractive complement to a legacy commercial gimbal controller tuning method in which the parameter tuning ranges are common for all possible hardware specifications of the gimbal irrespective of system stability. We compare the set of stabilizing PID controllers, called the stabilizing set, with a sample outcome of the autotuning algorithm provided with the commercial gimbal and verify that the stabilizing set contains the autotuning result. The geometrical visualization of the stabilizing set enables comparative analysis of the controllers, along with guide possible directions at which retuning should be aimed.

Keywords: Linear systems, PID control, Optimization
Abstract: In this paper we study delay robustness and tracking performance of PID controllers in stabilizing systems containing uncertain delays. In order to verify the potential tradeoff between the delay robustness and the tracking performance clear, we first propose a tracking performance assumption of concerned PID controllers. Next, we examine second-order unstable time-delay systems and seek the analytical characterization and exact computation of the delay margin. The delay margin defines the maximal range of delay within which the system can be robustly stabilized by a PID controller. In this paper, our contribution is twofold. First, we develop the analytical expressions, the efficient computation, and the explicit upper bounds of the PID delay margin achievable. The results also provide a well interpretation of the roles of three components of PID control on achieving the delay margin. Second, we prove that the higher the tracking accuracy is, the smaller a delay margin can be achieved, explaining well the tradeoff between delay robustness and tracking accuracy of PID controllers.

Keywords: PID control, Linear systems, Computer-aided control design
Abstract: The Proportional-Integral (PI) and Proportional Integral Derivative (PID) controller provide perfect steady state tracking and disturbance rejection of steps if the closed loop can be stabilized. The problem of achieving a "good" transient response over the stabilizing set remains a difficult open problem. In this paper we develop a technique to address this problem by assigning closed loop characteristic roots to prescribed regions of the complex plane. The specific regions chosen for study are a rectangle R, circle C and a triangle T. These regions reflect fast settling time (poles to the left of a line), small overshoot (poles to the right of a line) and limited frequency of oscillation (imaginary parts of poles within prescribed bounds). By using D-decomposition techniques and the Edge Theorem we attempt to determine useful subsets of the stabilizing set over which "good" transient response may be obtained. The results are illustrated by examples.

Keywords: PID control, Robotics, Stability of nonlinear systems
Abstract: In this paper, we study stability properties of Proportional-Derivative (PD) controlled underactuated robotic systems for trajectory tracking applications. Stability of PD control laws for fully actuated systems is an established result, and we extend it for the class of underactuated robotic systems. We will first show some well known examples where PD tracking control laws do not yield tracking; some of which can even lead to instability. We will then show that for a subclass of robotic systems, PD tracking control laws, indeed, yield desirable tracking guarantees. We will show that for a specified time interval, and for sufficiently large enough PD gains (input saturations permitting), local boundedness of the tracking error can be guaranteed. In addition, for a class of systems with the kinetic symmetry property, stronger conditions like convergence to desirable bounds can be guaranteed. This class is not restrictive and includes robots like the acrobot, the cart-pole, and the inertia-wheel pendulums. Towards the end, we will provide necessary simulation results in support of the theoretical guarantees presented.

Keywords: Optimization algorithms, LMIs, Optimization
Abstract: Compared to standard descent-based algorithms, accelerated first-order methods for strongly convex smooth optimization problems may exhibit large transient responses. For quadratic problems, this phenomenon arises from the presence of non-normal dynamics and the modes that yield an algebraic growth in early iterations. In this paper, we employ the framework of integral quadratic constraints to examine the transient response of Nesterov?s accelerated method. We prove that a bound on the largest value of the Euclidean distance between the optimization variable and the global minimizer is proportional to the square root of the condition number. For problems with large condition numbers we demonstrate tightness of this bound up to constant factors, thereby establishing the merits of our approach.

Keywords: Smart grid, Smart cities/houses, Learning
Abstract: We consider the problem of optimizing the cost of procuring electricity for a large collection of homes managed by a load serving entity, by pre-cooling or pre-heating the thermal inertial loads in the homes to avoid procuring power during periods of peak electricity pricing. We would like to accomplish this objective in a completely privacy-preserving and model-free manner, that is, without direct access to the state variables (temperatures or power consumption) or the dynamical models (thermal characteristics) of individual homes, while guaranteeing personal comfort constraints of the consumers. We propose a two-stage optimization and control framework to address this problem. In the first stage, we use a long short-term memory (LSTM) network to predict hourly electricity prices, based on historical pricing data and weather forecasts. Given the hourly price forecast and thermal models of the homes, the problem of designing an optimal power consumption trajectory that minimizes the total electricity procurement cost for the collection of thermal loads can be formulated as a large-scale integer program (with millions of variables) due to the on-off cyclical dynamics of such loads. We provide a simple heuristic relaxation to make this large-scale optimization problem model-free and computationally tractable. In the second stage, we translate the results of this optimization problem into distributed open-loop control laws that can be implemented at individual homes without measuring or estimating their state variables, while simultaneously ensuring consumer comfort constraints. We demonstrate the performance of this approach on a large-scale test case comprising of 500 homes in the Houston area and benchmark its performance against a direct model-based optimization and control solution.

Keywords: Optimization algorithms, Statistical learning, Estimation
Abstract: This paper considers a learning problem with heteroscedastic and correlated data that is distributed across nodes. We propose a distributed learning scheme where each node asynchronously implements stochastic gradient descent updates and exchanges their current models with neighbors. We ensure the similarity among the local models and the ensemble average by having a network regularization penalty to the least squares problem. This penalty is associated with weights that are proportional to the relative accuracy of local models. We provide finite time characterization of the disparity between local models and the ensemble average model based on the penalty constants and network connectivity. We compare the proposed method with generalized least squares and logistic regression in the prediction of activities of individuals based on head movement data.

Keywords: Optimization, Machine learning, Neural networks
Abstract: There has been an increasing interest in using neural networks in closed-loop control systems to improve performance and reduce computational costs for on-line implementation. However, providing safety and stability guarantees for these systems is challenging due to the nonlinear and compositional structure of neural networks. In this paper, we propose a novel forward reachability analysis method for the safety verification of linear time-varying systems with neural networks in feedback interconnection. Our technical approach relies on abstracting the nonlinear activation functions by quadratic constraints, which leads to an outer-approximation of forward reachable sets of the closed-loop system. We show that we can compute these approximate reachable sets using semidefinite programming. We illustrate our method in a quadrotor example, in which we first approximate a nonlinear model predictive controller via a deep neural network and then apply our analysis tool to certify finite-time reachability and constraint satisfaction of the closed-loop system.

Keywords: Identification, Nonlinear systems identification, Learning
Abstract: The paper proposes a practical method for a significant dimensionality reduction of Volterra kernels, defining a discrete nonlinear model of a signal by Volterra series of higher order. In system identification of Volterra series, the Volterra kernels and nonlinear inputs of the system can be described by super-symmetrical tensors. The reduction of their dimensionality is obtained by a tensor decomposition technique called Higher Order Singular Value Decomposition (HOSVD). The main contribution of the paper is a cascade learning algorithm for the system identification based on residuals of least squares minimization. Numerical examples for Volterra system of order four are used to illustrate the approach.

Keywords: Robotics, Autonomous robots, Predictive control for nonlinear systems
Abstract: This paper proposes an MPC-based controller to efficiently execute multiple hierarchical tasks for underactuated and constrained robotic systems. Existing task-space controllers or whole-body controllers solve instantaneous optimization problems given task trajectories and the robot plant dynamics. However, the task-space control method we propose here relies on the prediction of future state trajectories and the corresponding costs-to-go terms over a finite time-horizon for computing control commands. We employ acceleration energy error as the performance index for the optimization problem and extend it over the finite-time horizon of our MPC. Our approach employs quadratically constrained quadratic programming, which includes quadratic constraints to handle multiple hierarchical tasks, and is computationally more efficient than nonlinear MPC-based approaches that rely on nonlinear programming. We validate our approach using numerical simulations of a new type of robot manipulator system, which contains underactuated and constrained mechanical structures.

Keywords: Robotics, Autonomous systems
Abstract: Recently proposed Generalized Shape Expansion (GSE) algorithm for planning of shortest collision-free path in 2-D environments has shown significant promise in improvement of its performance over several seminal algorithms from existing literature. Recognizing that a suitable directional sampling feature could potentially enhance the performance of the GSE algorithm further, this paper proposes two sampling schemes - basic and augmented directional sampling - and presents GSE-D and GSE-AD algorithms, respectively, as expansion over the GSE. These algorithms, by default, enjoy the advantages of the GSE. Both the directional sampling schemes enable drawing random sample points with more preference towards the direction of the Goal leading to lower cost of computed shortest path on an average. While the basic directional sampling strategy faces a drawback in computational time when obstacle density in the direction towards the Goal is high, the augmented directional sampling scheme is free of this limitation. Probabilistic analysis and extensive numerical simulation studies show the effectiveness of the GSE-D and GSE-AD in performance in terms of computational time efficiency and shortest path cost when compared with the GSE, other seminal algorithms and existing directional algorithms.

Keywords: Vision-based control, Observers for nonlinear systems, Autonomous systems
Abstract: This paper focuses on a dual quaternion-based estimation and control approach for position-based visual servoing (PBVS). The pose estimation of the camera is achieved using a dual quaternion-based Extended Kalman Filter (EKF), which estimates the position and orientation of the camera based on feature points acquired through a sequence of camera images. Based on the estimation, a dual quaternion control law is developed to regulate the camera to the desired pose. Leveraging the local exponential stability of the EKF and the global exponential stability of the designed controller, a nonlinear separation principle is used to prove the stability of the joint estimation and control for PBVS. The method is distinguished from other PBVS methods in the sense that a compact representation of dual quaternion is used to represent the pose, and a joint stability of estimator and controller for PBVS in dual quaternion space is presented. The proposed dual quaternion PBVS method is validated using a simulation.

Keywords: Autonomous systems, Switched systems, Nonlinear systems identification
Abstract: A controller, estimator, and predictor framework is developed for tracking a moving target using a network of mobile cameras, with non-overlapping fields-of-views and operating regions. Using a Lyapunov-based switched systems approach, the proposed framework is proven to be robust to intermittent feedback, and estimates of the target?s pose and motion model are proven to remain bounded, provided that minimum and maximum dwell-time conditions are satisfied (i.e., minimum time the target must be observed and maximum time the target may be unobserved, respectively). This framework allows for teams of cooperative agents to track a moving target in complex environments, while increasing the effective target tracking area and guaranteeing tracking performance.

Keywords: Time-varying systems, Sensor networks, Optimization
Abstract: The use of online algorithms to track a moving target is gaining attention in the control community for its simpler and faster computation. In this work, we study the dynamic regret of online gradient descent (OGD) for tackling a time-of-arrival (TOA)-based least-squares formulation of the tracking problem. Since the formulation is non-convex, most existing dynamic regret analyses cannot be applied to it directly. To circumvent this difficulty, we proceed in two steps. First, we show that under standard assumptions on the TOA measurement noise, the loss function at each time step will, with high probability, be locally strongly convex at that time step. Moreover, we give an explicit estimate of the size of the strong convexity region. To the best of our knowledge, this result is new and can be of independent interest. Second, we show that under the aforementioned assumptions on the TOA measurement noise and mild assumptions on the target trajectory, the location estimate of the target at each time step will lie in the strong convexity region of the loss function at the next time step with high probability. This allows us to exploit existing analysis for online strongly convex optimization to give the first dynamic regret bound of OGD for the TOA-based target tracking problem. Simulation results are presented to illustrate our theoretical findings.

Keywords: Decentralized control, Machine learning, Optimization
Abstract: This paper considers a multi-armed bandit (MAB) problem in which multiple mobile agents receive rewards by sampling from a collection of spatially dispersed bandits. The goal is to formulate a decentralized policy for each agent, in order to maximize the total cumulative reward over all agents, subject to option availability and inter-agent communication constraints. Bandit locations are represented by vertices of the spatial graph. At any time, an agent's option consist of sampling the bandit at its current location, or traveling along an edge of the spatial graph to a new bandit location. Communication constraints are described by a directed, non-stationary, stochastic textit{communication graph}. At any time, agents may receive data only from their communication graph in-neighbors. In this paper, we propose a upper confidence bound based decentralized motion and option selection policy and a non-stationary stochastic communication protocol that guarantee logarithmic regret. To our knowledge, this is the first such decentralized policy for non-fully connected spatial graphs with communication constraints. When the spatial graph is fully connected and the communication graph is stationary, our decentralized algorithm matches or exceeds the best reported prior results from the literature.

Keywords: Decentralized control, Optimal control, Networked control systems
Abstract: We consider the problem of controlling a set of dynamically decoupled plants where the plants' subcontrollers communicate with each other according to a fixed and known network topology. We assume the communication to be instantaneous but there is a fixed processing delay associated with incoming transmissions. We provide explicit closed-form expressions for the optimal decentralized controller under these communication constraints and using standard LQG assumptions for the plants and cost function. Although this problem is convex, it is challenging due to the irrationality of continuous-time delays and the decentralized information-sharing pattern. Our solution describes the signals that plants should transmit across the network and the structure of the optimal subcontrollers, which consists of LTI and FIR blocks.

Keywords: Decentralized control, Stochastic optimal control, Mean field games
Abstract: We study stochastic team (known also as decentralized stochastic control or identical interest stochastic game) problems with large or countably infinite number of decision makers, and characterize existence and structural properties for (globally) optimal policies. We consider in particular both static and dynamic non-convex team problems where the cost function and dynamics satisfy an exchangeability condition. We first establish a de Finetti type representation theorem for exchangeable decentralized policies, that is, for the probability measures induced by admissible policies under decentralized information structures. For a general setup of stochastic team problems with N decision makers, under exchangeability of observations of decision makers and the cost function, we show that without loss of global optimality, the search for optimal policies over any convex set of probability measures on policies can be restricted to those that are N-exchangeable. Then, by extending N-exchangeable policies to infinitely exchangeable ones, establishing a convergence argument for the induced costs, and using the presented de Finetti type theorem, we establish the existence of an optimal decentralized policy for static and dynamic teams with countably infinite number of decision makers, which turns out to be symmetric (i.e., identical) and randomized. In particular, unlike prior work, convexity of the cost is not assumed.

Keywords: Linear systems, Decentralized control, Computational methods
Abstract: The paper proposes a method for structured state-feedback controllers design for linear time-invariant systems. A necessary and sufficient condition for structured state-feedback stabilizability of linear systems, making an appeal to the linear-quadratic (LQ) regulator theory, is first proposed. The latter is presented in the form of a nonlinear matrix equation. Then, it is recast as a non-smooth unconstrained equation using projection onto the positive semi-definite matrices cone. Thereby, a non-smooth Newton's iterative algorithm, based on the Clarke generalized Jacobian of said projection, is proposed. This method has a guaranteed local convergence. Finally, numerical examples illustrate the effectiveness of the proposed method.

Keywords: Decentralized control, Predictive control for linear systems
Abstract: We address the problem of synthesizing state- constraint sets for a fully decentralized Model Predictive Control (MPC) scheme. We consider linear time-invariant discrete time systems, with subsystems possibly coupled in both dynamics and state constraints. For each individual subsystem we employ a set-based framework to compute the state-constraint sets, that are used to synthesize local tube- based MPC controllers. The offline problem that computes the constraint sets explicitly ensures that the feasible regions of the MPC controllers are non-empty, and whenever the controllers are feasible, the overall system constraints are satisfied with the least conservativeness possible. We demonstrate the closed-loop performance of the decentralized scheme, assessed with respect to centralized MPC, using a numerical example.

Keywords: Linear systems, Identification
Abstract: As far as direct data-driven design is concerned, no matter the design approach to be exploited, the objective of the control problem is to make the closed-loop system to match, as close as possible, the behavior of an assigned reference model M. In this work, we investigate the problem of designing a suitable reference model M by using the Hinfinity control techniques. More specifically, we propose a procedure that provides a reference model guaranteed to fulfill a number of quantitative performance requirements for both minimum-phase (MP) and non-minimum phase (NMP) stable plant, by solving a suitably formulated fictitious Hinfinity control problem. The effectiveness of the presented technique is demonstrated by means of a simulation example using the set-membership based direct data-driven control approach.

Keywords: Optimal control, Constrained control, Direct adaptive control
Abstract: This paper presents a data-driven algorithm to solve the problem of infinite-horizon linear quadratic regulation (LQR), for a class of discrete-time linear time-invariant systems subjected to state and control constraints. The problem is divided into a constrained finite-horizon LQR subproblem and an unconstrained infinite-horizon LQR subproblem, which can be solved directly from collected input/state data, separately. Under certain conditions, the combination of the solutions of the subproblems converges to the optimal solution of the original problem. The effectiveness of the proposed approach is validated by a numerical example.

Keywords: Robust control, Uncertain systems, Identification for control
Abstract: This paper considers the problem of designing state feedback data-driven controllers for nonlinear continuous-time systems. Specifically, we consider a scenario where the unknown dynamics can be parametrized in terms of known basis functions and the available measurements are corrupted by unknown-but-bounded noise. The goal is to use this noisy experimental data to directly design a rational state-feedback control law guaranteed to stabilize all plants compatible with the available information. The main result of the paper shows that, by using Rantzer's Dual Lyapunov approach, combined with elements from convex analysis, the problem can be recast as an optimization over positive polynomials, which can be relaxed to a semi-definite program through the use of Sum of Squares (SoS) and semi-algebraic optimization arguments.

Keywords: Stability of nonlinear systems, Optimization algorithms, Optimal control
Abstract: In this letter, we propose a bio-inspired derivativefree optimization algorithm capable of minimizing objective functions with vanishing or exploding gradients. The proposed method searches for improvements by leveraging a PCA-based strategy similar to fish foraging. The strategy does not require explicit gradient computation or estimation and is shown in simulation to require few function evaluations. Additionally, our analysis proves that the proposed algorithm?s search direction converges to the gradient direction everywhere outside of small neighborhoods around local minima. Applications to a data-driven LQR problem and noisy Rosenbrock optimization problem are demonstrated. Empirical results show the proposed method exhibits fast convergence and is able to find the LQR gains for any controllable system, including unstable systems, and is robust to noisy function evaluations.

Keywords: Pattern recognition and classification, Optimization, Fault diagnosis
Abstract: Feature selection is an important task in data-driven control applications to identify relevant features and remove non-informative ones, for example residual selection for fault diagnosis. For multi-class data, the objective is to find a minimal set of features that can distinguish data from all different classes. A distributed feature selection algorithm is derived using convex optimization and the Alternating Direction Method of Multipliers. The distributed algorithm scales well with increasing number of classes by utilizing parallel computations. Two case studies are used to evaluate the developed feature selection algorithm: fault classification of an internal combustion engine and the MNIST data set to illustrate a larger multi-class classification problem.

Keywords: Linear systems, Observers for Linear systems
Abstract: This paper presents distance measures for strong observability and strong detectability of linear, time-invariant systems with direct feedthrough. In contrast to standard binary criteria, the proposed measures allow to quantify these properties numerically. An optimization based approach for calculating the measures is derived. Meaningful conditions for such measures are introduced and the properties of the proposed measures regarding these conditions are analyzed. In order to demonstrate their usefulness, the measures are applied to optimal sensor placement for reconstruction of unknown forces on a mechanical structure.

Keywords: Observers for Linear systems, Linear systems, Time-varying systems
Abstract: In this work, we present a novel fixed-time state observer for LTI systems based on a time-varying coordinate transformation yielding the cancellation of the effect of the unknown initial conditions from the state estimates. This coordinate transformation allows one to map the state of the original system into that of an auxiliary system that evolves from initial conditions that are known by construction. After a stable observer is designed in the transformed coordinates, an estimate for the state of the original system can be obtained by inverting the above-mentioned map. The invertibility of the map is guaranteed for any time strictly greater than zero, so that the convergence time can be made arbitrarily small in nominal conditions. The robustness of the observer with respect to bounded measurement disturbances is characterized in terms of both transient and norm bounds on the asymptotic state-estimation error. Compared to existing finite and fixed-time approaches, the proposed method does not require high-gain output-error injection, state augmentation, delay operators, or moving-windows. The dimensionality of the observer matches that of the observed system, and its realization takes the form of an LTV system.

Keywords: Observers for Linear systems, Estimation, LMIs
Abstract: In this paper, we simultaneously determine the optimal sensor precision and the observer gain, which achieves the specified accuracy in the state estimates. Along with the unknown observer gain, the formulation parameterizes the scaling of the exogenous inputs that correspond to the sensor noise. Reciprocal of this scaling is defined as the sensor precision, and sparseness is achieved by minimizing the l1 norm of the precision vector. The optimization is performed with constraints guaranteeing specified accuracy in state estimates, which are defined in terms of H2 or H-infinity norms of the error dynamics. The results presented in this paper are applied to the linearized longitudinal model of an F-16 aircraft.

Keywords: Observers for Linear systems, Large-scale systems, Networked control systems
Abstract: State variance of a network system is a nonlinear functional computed as the squared deviation of the network's state vector. Such a quantity is useful to monitor how much the states of network nodes are spread around their average mean. Estimating state variance is crucial when the full state estimation of a network system is not possible due to limited computational and sensing resources. We propose a novel methodology to estimate the state variance in a computationally efficient way. First, clusters are identified in the network such that the state variance can be approximated from the average states of the clusters. Then, the approximated state variance is estimated from the average state observer.

Keywords: Observers for Linear systems, Attack Detection, Estimation
Abstract: This paper addresses the problem of estimation of the average state of an LTI network system where measurements of only some of the states are available. We consider the case where there is an outlier among the unmeasured states, which is so different from the remaining states that it affects the average value significantly. The goal of this paper is to detect the outlier and to estimate the average of the unmeasured states excluding the outlier.

Keywords: Optimization algorithms, Predictive control for linear systems
Abstract: In this paper we propose a method to exactly certify the complexity of an active-set method which is based on reformulating strictly convex quadratic programs to nonnegative least-squares problems. The exact complexity of the method is determined by proving the correspondence between the method and a standard primal active-set method for quadratic programming applied to the dual of the quadratic program to be solved. Once this correspondence has been established, a complexity certification method which has already been established for the primal active-set method is used to also certify the complexity of the nonnegative least-squares method. The usefulness of the proposed method is illustrated on a multi-parametric quadratic program originating from model predictive control of an inverted pendulum.

Keywords: Optimization
Abstract: This paper considers a hybrid risk measure for decision-making under uncertainties that tradeoffs between the solutions obtained from the robust optimization and the stochastic optimization techniques. In the proposed framework, the risk measure is shown to satisfy the properties of coherent risk measures. The level of guaranteed robustness can be controlled by a parameter. We formulate the stochastic and robust optimization problem under the proposed risk measure and show the equivalent formulation and sensitivity result. We introduce the sampled approximation of the technique by combining scenario program and sample average approximation, making it amenable for practical usage. We present a supervised learning problem as a case study to corroborate our results and show the implications of the proposed method of machine learning.

Keywords: Optimization algorithms, Machine learning, Power systems
Abstract: We extend the regret analysis of the online distributed weighted dual averaging (DWDA) algorithm from Hosseini et al. to the dynamic setting and provide the tightest dynamic regret bound known to date with respect to the time horizon for a distributed online convex optimization (OCO) algorithm. Our bound is linear in the cumulative difference between consecutive optima and does not depend explicitly on the time horizon. We use dynamic-online DWDA (D-ODWDA) and formulate a performance-guaranteed distributed online demand response approach for heating, ventilation, and air-conditioning (HVAC) systems of commercial buildings. We show the performance of our approach for fast timescale demand response in numerical simulations and obtain demand response decisions that closely reproduce the centralized optimal ones.

Keywords: Optimization algorithms, Sensor networks, Randomized algorithms
Abstract: We present a distributed optimization protocol that preserves statistical privacy of agents? local cost functions against a passive adversary that corrupts some agents in the network. The protocol is a composition of a distributed ?zero-sum? obfuscation protocol that obfuscates the agents? local cost functions, and a standard non-private distributed optimization method. We show that our protocol protects the statistical privacy of the agents? local cost functions against a passive adversary that corrupts up to t arbitrary agents as long as the communication network has (t + 1)-vertex connectivity. The ?zero-sum? obfuscation protocol preserves the sum of the agents? local cost functions and therefore ensures accuracy of the computed solution.

Keywords: Control applications, Predictive control for linear systems, Optimization algorithms
Abstract: Fair power allocation for temperature regulation in the heating, ventilation and air conditioning (HVAC) system of a multi-unit building is investigated in this paper. The temperature of each unit is described by a discrete-time dynamic equation, taking into account the effect of outside temperature as well as heat-transfer between the adjacent rooms. Temperature regulation is then formulated as a constrained optimization problem, where the objective is to maintain the temperature of each unit within a prescribed thermal comfort zone with the limited amount of available power. An optimal control strategy is presented to minimize the maximum mutual temperature difference between different units (long-term fairness) while maintaining the temperature of each unit in the comfort zone or close to it at all times, as much as possible (short-term fairness). Simulations demonstrate the effectiveness of the proposed control strategy in regulating the temperature of every unit in a building.

Keywords: Fuzzy systems, Robust control
Abstract: In this paper, the issue of disturbance rejection of nonlinear repetitive control system (RCS) based on a continuous-discrete two-dimensional (2D) model is studied. Since a RCS involves continuous control and discrete learning, higher tracking performance may be realizable by taking into account these two different actions in system design. This paper construct a fuzzy RCS based on T-S model at first. Then, an improved fuzzy-equivalent-input-disturbance (IFEID)-based 2D RCS is presented to achieve both high tracking precision of periodic input and satisfactory rejection of aperiodic disturbances. Stability conditions of two subsystems are derived by exploiting separation theorem to ease the solution of state-feedback and observer gains. A design algorithm is presented via the concept of parallel distributed compensation. A simulation and a comparison demonstrate the availability and advantage of the IFEID-based 2D RCS approach.

Keywords: Fuzzy systems, Estimation, Lyapunov methods
Abstract: This paper presents a discrete-time Takagi-Sugeno fuzzy observer design approach for a class of nonlinear systems. Instead of including all the nonlinear terms in the membership functions, some of them are kept as nonlinear consequents, and they need to fulfill a global Lipschitz condition. The form considered permits nonlinear consequents that depend on nonscalar inputs. The design conditions are defined in terms of linear matrix inequalities, and they are less restrictive than previous conditions from the literature. Two numerical examples highlight the advantages obtained.

Keywords: Fuzzy systems, Estimation, Lyapunov methods
Abstract: This paper investigates the design of unknown input (UI) observers for a large class of nonlinear systems using Takagi-Sugeno (TS) fuzzy modeling. To avoid the well-known issue on the unmeasured premise variables in fuzzy observer design, we reformulate the nonlinear systems in a TS fuzzy form with local nonlinear models. A particular feature of these so-called N-TS fuzzy models is that all the unmeasured nonlinearities are isolated in a nonlinear consequent. Together with a judicious use of the differential mean value theorem, the N-TS fuzzy reformulation enables an effective framework to design fuzzy UI observers. Based on an UI decoupling technique, no specific information on the UI is required for fuzzy observer design. The asymptotic estimations of both the state and the UI are guaranteed with fuzzy Lyapunov arguments. The observer gains can be effectively computed following an LMI-based design procedure. The interest of the proposed method over related existing results is demonstrated with a physical example.

Keywords: Networked control systems, Fuzzy systems
Abstract: This article studies the reduced-order filters design issue for networked T-S fuzzy systems with an adaptive eventtriggered mechanism (AETM). Attention is concentrated on constructing lower-order filter error systems that approximate the original ones with H∞, L2-L∞, passive and dissipative performance in a unified framework. Moreover, an AETM, whose communication threshold is adaptively updated based on latest released data, is introduced to reduce communication number. Unlike some existing results, a novel membershipfunction-dependent fuzzy Lyapunov-Krasovsikii function is considered to obtain better extended dissipative performance. A switching method is proposed to cope with the time derivative of membership functions (MFs), and then, based on their signs, a switching fuzzy reduced-order filter is constructed to stabilize the system. Finally, an example is considered to demonstrate the effectiveness of the given results.

Keywords: Observers for nonlinear systems, Fuzzy systems, Estimation
Abstract: This paper discusses a new approach to overcome unmeasurable premise variables in observer synthesis for Takagi- Sugeno models. The main idea is based on the decoupling of the nonlinear dynamics in order to manage unmeasured state existing into the membership functions. The obtained structure is a system with membership functions subjected only to measured variables. The stability analysis of the observer is carried out using Lyapunov theory. The observer gains were computed from the resolution of the Linear Matrix Inequality constraints. The present result alleviates the strong conditions assumed in the design of observers for TS systems with unmeasurable premise variables. Simulation results are provided to demonstrate the effectiveness of the proposed approach.

Keywords: Decentralized control, Machine learning, Neural networks
Abstract: Multi-agent reinforcement learning (MARL) under partial observability has long been considered challenging, primarily due to the requirement for each agent to maintain a belief over all other agents' local histories -- a domain that generally grows exponentially over time. In this work, we investigate a partially observable MARL problem in which agents are cooperative. To enable the development of tractable algorithms, we introduce the concept of an information state embedding that serves to compress agents' histories. We quantify how the compression error influences the resulting value functions for decentralized control. Furthermore, we propose an instance of the embedding based on recurrent neural networks (RNNs). The embedding is then used as an approximate information state, and can be fed into any MARL algorithm. The proposed embed-then-learn pipeline opens the black-box of existing (partially observable) MARL algorithms, allowing us to establish some theoretical guarantees (error bounds of value functions) while still achieving competitive performance with many end-to-end approaches.

Keywords: Optimization, Optimization algorithms, Computational methods
Abstract: We study multimarginal optimal transport (MOT) problems, which include, as a particular case, the Wasserstein barycenter problem. In MOT problems, one has to find an optimal coupling between m probability measures, which amounts to finding a tensor of order m. We propose a method based on accelerated alternating minimization and estimate the complexity to find an approximate solution. We use entropic regularization with a sufficiently small regularization parameter and apply accelerated alternating minimization to the dual problem. A novel primal-dual analysis is used to reconstruct the approximately optimal coupling tensor. Our algorithm exhibits a better computational complexity than the state-of-the-art methods for some regimes of the problem parameters.

Keywords: Network analysis and control, Networked control systems, Control of networks
Abstract: In this paper we study a discrete-time SIS (susceptible-infected-susceptible) model, where the infection and healing parameters and the underlying network may change over time. We provide conditions for the model to be well-defined and study its stability. For systems with homogeneous infection rates over symmetric graphs, we provide a sufficient condition for global exponential stability (GES) of the healthy state, that is, where the virus is eradicated. For systems with heterogeneous virus spread over directed graphs, provided that the variation is not too fast, a sufficient condition for GES of the healthy state is established. Appealing to the first stability result, we present two data-driven mitigation strategies that set the healing parameters in a centralized and a distributed manner, respectively, in order to drive the system to the healthy state.

Keywords: Stochastic systems, Optimization algorithms, Communication networks
Abstract: Communication plays a vital role for distributed computation over networks, but practical communication networks are random due to link failures, packet dropouts or node recreation, probably with both temporal and spatial dependence. To understand how generic random networks influence distributed computation, we consider distributedly solving linear equations over a *-mixing random network,where each node holds a part of problem data. We investigate the distributed projection consensus algorithm, prove the almost sure convergence to a consensual solution as a function of initial states, and show the exponential convergence rate of the mean-squared error when the network linear equation admits exact solutions. We further give an explicit convergence rate of the mean-squared error with an estimation of the lower and upper bounds for independent and identically distributed (i.i.d.) random graphs. Simulation studies are provided.

Keywords: Agents-based systems, Networked control systems, Cooperative control
Abstract: This paper aims to solve the distributed convex optimization problem for a class of multi-agent systems (MASs) with event-triggered communication and attacks on communication edges. Specifically, the local objective functions for agents are assumed to be strongly convex and continuously differentiable with Lipschitz continuous gradients. Unlike most of the MAS models considered in the existing literature, the attacks on communication edges among neighboring agents are considered and the effect of such attacks on optimal solution seeking is further analyzed. To solve such an optimization problem with relatively low communication cost among agents, a new kind of event-triggered optimization protocol is proposed for each agent. Sufficient yet efficient conditions are derived to ensure that the states of all agents exponentially converge to the optimal solution of the group objective function (i.e., the sum of all local objective functions). Furthermore, it is proved that the Zeno-behavior is excluded during the evolution of the MASs. Finally, some simulation studies are provided to illustrate the efficiency of the proposed event-triggered optimization protocol.

Keywords: Uncertain systems, Stability of linear systems, Robust control
Abstract: This paper is concerned with robust instability analysis of linear feedback systems subject to a dynamic uncertainty. The work is motivated by, and provides a basic foundation for, a more challenging problem of analyzing persistence of oscillations in nonlinear dynamical systems. We first formalize the problem for SISO LTI systems by introducing a notion of the robust instability radius (RIR). We provide a method for calculating the RIR exactly for a certain class of systems and show that it works well for a class of second order systems. This result is applied to the FitzHugh-Nagumo model for neuronal dynamics, and the effectiveness is confirmed by numerical simulations, where we properly care for the change of the equilibrium point.

Keywords: Biological systems, Agents-based systems, Network analysis and control
Abstract: Cortical regions without direct neuronal connections have been observed to exhibit synchronized dynamics. A recent empirical study has further revealed that such regions that share more common neighbors are more likely to behave coherently. To analytically investigate the underlying mechanisms, we consider that a set of n oscillators, which have no direct connections, are linked through m intermediate oscillators (called mediators), forming a complete bipartite network structure. Modeling the oscillators by the Kuramoto-Sakaguchi model, we rigorously prove that mediated remote synchronization, i.e., synchronization between those n oscillators that are not directly connected, becomes more robust as the number of mediators increases. Simulations are also carried out to show that our theoretical findings can be applied to other general and complex networks.

Keywords: Biological systems, Network analysis and control, Nonlinear output feedback
Abstract: Biophysical coupling in neuronal networks is either through gap junctions or synapses. This paper explores how models of synaptic coupling relate to the standard diffusive coupling model studied in the control theory of networks. In particular, we investigate how weak synaptic coupling can locally realize strong diffusive coupling in the vicinity of nonlinear oscillations of the relaxation type. Although often perceived as a source of complexity, the combination of nodal excitability with synaptic coupling is shown to be a source of tractability, allowing for robust mathematical predictions on the basis of linear analysis.

Keywords: Biological systems, Robust control, Compartmental and Positive systems
Abstract: Neuronal systems exhibit highly stable and tuneable behaviors in spite of huge variability at the molecular component level and in spite of persistent physiological and pathological perturbations. How is this robust flexibility achieved? Homeostatic integral control has been shown to be key in reconciling variability with stability, but the explanatory model used lacks basic robustness properties. We suggest that positive molecular regulatory networks may play a major role in reconciling stability, variability {it and} robustness. The main control theoretical idea we propose is that integral control happens along the dominant direction of the network. This slow direction generates a strongly attractive, and thus robust, subspace along which almost perfect homeostatic regulation can be achieved. Fluctuations of relevant molecular variables along this slow subspace explain how variability is compatible with robust regulation, thus explaining flexibility. Because of robustness, the properties of the positive network can be subject to slower tuning processes (like the circadian rhythm), which provides a biologically plausible basis for tuneable variability to be compatible with robust regulation. The relevance of the proposed regulation model for control-theoretical approaches to neurological diseases is also discussed.

Keywords: Closed-loop identification, Nonlinear systems identification, Neural networks
Abstract: After sixty years of quantitative biophysical modeling of neurons, the identification of neuronal dynamics from input-output data remains a challenging problem, primarily due to the inherently nonlinear nature of excitable behaviors. By reformulating the problem in terms of the identification of an operator with fading memory, we explore a simple approach based on a parametrization given by a series interconnection of Generalized Orthonormal Basis Functions (GOBFs) and static Artificial Neural Networks. We show that GOBFs are particularly well-suited to tackle the identification problem, and provide a heuristic for selecting GOBF poles which addresses the ultra-sensitivity of neuronal behaviors. The method is illustrated on the identification of a bursting model from the crab stomatogastric ganglion.

Keywords: Robust adaptive control, Optimal control, Predictive control for linear systems
Abstract: A dual adaptive model predictive control (MPC) algorithm is presented for linear, time-invariant systems subject to bounded disturbances and parametric uncertainty in the state-space matrices. Online set-membership identification is performed to reduce the uncertainty and thus control affects both the informativity of identification and the system's performance. The main contribution of the paper is to include this dual effect in the MPC optimization problem using a predicted worst-case cost in the objective function. This allows the controller to perform active exploration, that is, the control input reduces the uncertainty in the regions of the parameter space that have most influence on the performance. Additionally, the MPC algorithm ensures robust constraint satisfaction of state and input constraints. Advantages of the proposed algorithm are shown by comparing it to a passive adaptive MPC algorithm from the literature.

Keywords: Automotive control, Learning, Autonomous vehicles
Abstract: A good racing strategy and, in particular, the racing line is decisive to winning races in Formula 1, MotoGP, and other forms of motor racing. The racing line defines the path followed around a track and the optimal speed profile along the path. The objective is to minimize lap time by driving the vehicle at the limits of friction and handling capability. The solution naturally depends upon the geometry of the track and vehicle dynamics. We introduce a novel method to compute the racing line using Bayesian optimization. Our approach is fully data- driven and computationally more efficient compared to other methods based on dynamic programming and naive random search. The approach is specifically relevant in autonomous racing, where teams can quickly compute the racing line for a new track and then exploit this information to design a motion planner and a controller to optimize real-time performance.

Keywords: Decentralized control, Iterative learning control, Predictive control for nonlinear systems
Abstract: We present a decentralized minimum-time trajectory optimization scheme based on learning model predictive control for multi-agent systems with nonlinear decoupled dynamics and coupled state constraints. By performing the same task iteratively, data from previous task executions is used to construct and improve local time-varying safe sets and an approximate value function. These are used in a decoupled MPC problem as terminal sets and terminal cost functions. Our framework results in a decentralized controller, which requires no communication between agents over each iteration of task execution, and guarantees persistent feasibility, finite-time closed-loop convergence, and non-decreasing performance of the global system over task iterations. Numerical experiments of a multi-vehicle collision avoidance scenario demonstrate the effectiveness of the proposed scheme.

Keywords: Iterative learning control, Linear systems, Predictive control for linear systems
Abstract: We propose a control design method for linear time-invariant systems that iteratively learns to satisfy unknown polyhedral state constraints. At each iteration of a repetitive task, the method constructs an estimate of the unknown environment constraints using collected closed-loop trajectory data. This estimated constraint set is improved iteratively upon collection of additional data. An MPC controller is then designed to robustly satisfy the estimated constraint set. This paper presents the details of the proposed approach, and provides robust and probabilistic guarantees of constraint satisfaction as a function of the number of executed task iterations. We demonstrate the safety of the proposed framework and explore the safety vs. performance trade-off in a numerical example.

Keywords: Stochastic optimal control, Statistical learning, Uncertain systems
Abstract: This paper studies the sample complexity of the stochastic Linear Quadratic Regulator when applied to systems with multiplicative noise. We assume that the covariance of the noise is unknown and estimate it using the sample covariance, which results in a larger closed-loop cost. The main contribution of this paper is then to bound the suboptimality of the methodology --- i.e., the difference between the closed-loop cost and the true optimum --- and prove that it decreases with 1/N, where N denotes the amount of samples of the noise distribution. Under certain assumptions, the methodology is also applicable when only state trajectories are available. It also generalizes to the case where the mean is unknown and to the distributionally robust case studied in a previous work of the authors. The analysis is mostly based on results from matrix function perturbation analysis.

Keywords: Optimal control, Sampled-data control, Adaptive control
Abstract: This paper develops a novel optimal recursive backstepping design for the optimal regulation of a class of nonlinear systems in a strict-feedback form. In contrast to classical backstepping design, the presented recursive design takes the optimality of the solution into account. It is shown that the optimal recursive design results in the asymptotic stability of the equilibrium point for the isolated systems and ultimate boundedness for the cascade systems. In addition to the optimal recursive backstepping control design with continuous feedback, the optimal intermittent feedback design is also considered.

Keywords: Optimization, Agents-based systems, Cooperative control
Abstract: In this paper, we study the distributed optimisation problem {in which multiple agents cooperatively and distributively solve an optimisation problem. In order to avoid continuous communication among agents}, we propose a stochastic distributed dynamic event-triggering law to schedule the communication. We show that the optimisation problem can be solved with exponential rate and arbitrarily small optimisation error. {We further prove that Zeno behaviour does not exist in the proposed stochastic event-triggering law by constructing a lower bound on the inter-event interval which is essential for the feasibility of proposed algorithm.} A numerical simulation is presented to illustrate the effectiveness of the proposed algorithm when compared with some existing event-triggered distributed optimisation algorithms.

Keywords: Statistical learning, Control over communications, Networked control systems
Abstract: We study a setting where each agent in a network receives certain private signals generated by an unknown static state that belongs to a finite set of hypotheses. The agents are tasked with collectively identifying the true state. To solve this problem in a communication-efficient manner, we propose an event-triggered distributed learning algorithm that is based on the principle of diffusing low beliefs on each false hypothesis. Building on this principle, we design a trigger condition under which an agent broadcasts only those components of its belief vector that have adequate innovation, to only those neighbors that require such information. We establish that under standard assumptions, each agent learns the true state exponentially fast almost surely. We also identify sparse communication regimes where the inter-communication intervals grow unbounded, and yet, the asymptotic learning rate of our algorithm remains the same as when agents communicate at every time-step. We then establish, both in theory and via simulations, that our event-triggering strategy has the potential to significantly reduce information flow from uninformative agents to informative agents. Finally, we argue that, as far as only asymptotic learning is concerned, one can allow for arbitrarily sparse communication patterns.

Keywords: Networked control systems, Hybrid systems, Stability of hybrid systems
Abstract: In this paper, general conditions for set stabilization of (distributed) event-triggered control systems affected by measurement noises are presented. It is shown that, under these conditions, both static and dynamic triggers can be designed using a space-regularization approach such that the closed-loop system ensures an input-to-state practical stability property. Additionally, by proper choice of the tuning parameters, the system does not exhibit Zeno behavior. Contrary to various results in the literature, the noises do not have to be differentiable. The general results are applied to point stabilization and consensus problems as particular cases. Simulations illustrate our results.

Keywords: Agents-based systems, Resilient Control Systems, Cyber-Physical Security
Abstract: The paper considers the problem of multi-agent consensus in the presence of adversarial agents which may try to prevent and introduce undesired influence on the coordination among the regular agents. To our setting, we extend the socalled mean subsequence reduced algorithms with the aim to reduce the amount of communication via two measures: The agents exchange information in the form of ternary data at each transmission and moreover keep the frequency of data exchange low by employing self- and event-triggered communication. We will observe that in hostile environments with adversaries, the self-triggered approach can bring certain advantages over the event-triggered counterpart.

Keywords: Control Systems Privacy, Agents-based systems, Quantized systems
Abstract: In this paper, we propose a privacy-preserving event-triggered quantized average consensus algorithm that allows agents to calculate the average of their initial values without revealing to other agents their specific value.We assume that agents (nodes) interact with other agents via directed communication links (edges), forming a directed communication topology (digraph). The proposed distributed algorithm can be followed by any agent wishing to maintain its privacy (i.e., not revealing the initial value it contributes to the average) to others, possibly multiple, curious but not malicious agents. Curious agents try to identify the initial values of other agents, but do not interfere in the computation. We develop a distributed strategy that allows agents while processing and transmitting quantized information, to preserve the privacy of their initial quantized values and at the same time to obtain, after a finite number of steps, the exact average of the initial values of the nodes. Illustrative examples demonstrate the validity and performance of our proposed algorithm.

Keywords: Control Systems Privacy, Distributed control, Estimation
Abstract: The nature of information sharing in common distributed consensus algorithms permits network eavesdroppers to expose sensitive system information. An important parameter within distributed systems, often neglected under the scope of privacy preservation, is the influence structure - the weighting each agent places on the sources of their opinion pool. This paper proposes a local (i.e. computed individually by each agent), time varying mask to prevent the discovery of the influence structure by an external observer with access to the entire information flow, network knowledge and mask formulation. This result is produced through the auxiliary demonstration of the preserved stability of a Friedkin-Johnsen system under a set of generalised conditions. The mask is developed under these constraints and involves perturbing the influence structure by decaying pseudonoise. This paper provides the information matrix of the best influence structure estimate by an eavesdropper lacking a priori knowledge and uses stochastic simulations to analyse the performance of the mask against ranging system hyperparameters.