Keywords: Mean field games, Game theory, Stochastic optimal control
Abstract: In this paper, we present a brief tutorial on risk-aware control and game theory applied to engineering problems by solving a backward-forward partial-integro differential system composed of the Hamilton-Jacobi-Bellman and Fokker-Planck coupled equations. First, we discuss about the role that risk terms play in the engineering field. Then, both the risk-aware control and game problems are stated and the computation of the corresponding solutions is presented. We mainly focus on the propagation regulation of the coronavirus disease using mean-field-type control. Hence, we discuss other engineering applications that can be addressed by using the same risk-aware perspective. Among such applications, we discuss about the electric vehicles, and the bio-inspired collective decision-making.

Keywords: Mean field games, Biological systems, Large-scale systems
Abstract: This talk mainly focuses on the propagation regulation of the coronavirus disease using mean-field type control.

Keywords: Mean field games, Biologically-inspired methods, Markov processes
Abstract: Motivated by honeybee swarms, we consider a population of players that have to reach agreement on two equally favourable options. The problem results in a continuous-time discrete state mean-field game model . Model misspecifications are accounted by an additional adversarial disturbance. We discuss existence and computation of stationary solutions.

Keywords: Game theory, Mean field games, Automotive systems
Abstract: We introduce responsive loads for a population of electric vehicles. The vehicles are designed to obtain their optimal charging policies in an autonomous fashion by calculating best-responses to the population behavior. We discuss mean-field equilibium points and investigate ways in which we can obtain an approximation of such equilibrium point via simple calculations. The methodology involves turning the game into a sequence of data-driven infinite horizon receding horizon optimization problems that each vehicle solves online.

Keywords: Mean field games, Markov processes, Switched systems
Abstract: This talk focuses on the role of asymptomatic individuals in spreading COVID-19 disease. We extend the susceptible-infected-recovered model to capture the interactions of individuals via complex networks.

Keywords: Network analysis and control, Control of networks
Abstract: In this letter, we propose an epidemic model over temporal networks that explicitly encapsulates two different control actions. We develop our model within the theoretical framework of activity driven networks (ADNs), which have emerged as a valuable tool to capture the complexity of dynamical processes on networks, coevolving at a comparable time scale to the temporal network formation. Specifically, we complement a susceptible-infected-susceptible epidemic model with features that are typical of nonpharmaceutical interventions in public health policies: i) actions to promote awareness, which induce people to adopt self-protective behaviors, and ii) confinement policies to reduce the social activity of infected individuals. In the thermodynamic limit of large-scale populations, we use a mean-field approach to analytically derive the epidemic threshold, which offers viable insight to devise containment actions at the early stages of the outbreak. Through the proposed model, it is possible to devise an optimal epidemic control policy as the combination of the two strategies, arising from the solution of an optimization problem. Finally, the analytical computation of the epidemic prevalence in endemic diseases on homogeneous ADNs is used to optimally calibrate control actions toward mitigating an endemic disease. Simulations are provided to support our theoretical results.

Keywords: Control of networks, Compartmental and Positive systems, Large-scale systems
Abstract: In this letter we propose a method for sparse allocation of resources to control spreading processes - such as epidemics and wildfires - using convex optimization, in particular exponential cone programming. Sparsity of allocation has advantages in situations where resources cannot easily be distributed over a large area. In addition, we introduce a model of risk to optimize the product of the likelihood and the future impact of an outbreak. We demonstrate with a simplified wildfire example that our method can provide more targeted resource allocation compared to previous approaches based on geometric programming.

Keywords: Biological systems, Identification, Observers for nonlinear systems
Abstract: This paper aims to identify the parameters of an original modified SEIR model for the COVID-19 epidemic’s course in France by using publicly available data and applying such an identified model for the prediction of the SARS-CoV-2 virus propagation under different conditions of confinement. For this purpose, an interval predictor is designed, allowing variations and uncertainties in the model parameters to be taken into account.

Keywords: Biological systems, Nonlinear systems identification, Modeling
Abstract: The purpose of this work is to give a contribution to the understanding of the COVID-19 contagion in Italy. To this end, we developed a modified Susceptible-Infected-Recovered (SIR) model for the contagion, and we used official data of the pandemic up to March 30th, 2020 for identifying the parameters of this model. The non standard part of our approach resides in the fact that we considered as model parameters also the initial number of susceptible individuals, as well as the proportionality factor relating the detected number of positives with the actual (and unknown) number of infected individuals. Identifying the contagion, recovery and death rates as well as the mentioned parameters amounts to a non-convex identification problem that we solved by means of a two-dimensional grid search in the outer loop, with a standard weighted least-squares optimization problem as the inner step.

Keywords: Biological systems, Adaptive systems, Iterative learning control
Abstract: This paper shows that visuomotor adaptation can be cast as a disturbance rejection problem. We begin by formalizing experimentally observed dynamic properties of adaptation in terms of the transient response of a stable linear system, and we discuss implications on the validity of classes of models. Next, we solve the visuomotor adaptation problem by invoking adaptive internal models. A theoretical result on stability is obtained using averaging theory. Simulations applied to a visuomotor rotation experiment with fast arm reaches show that the dynamic properties of adaptation are recovered using our model.

Keywords: Biological systems, Algebraic/geometric methods, Stability of nonlinear systems
Abstract: Scientists have long been attracted to mechanisms surrounding the predator-prey system. The Lotka--Volterra (LV) model is the most popular formalism used to investigate the dynamics of this system. LV equations present non-linear dynamics that exhibit periodic oscillations in both prey and predator populations. In practical situations, it is useful to stabilise the system asymptotically to a desired set point (population) wherein the two species coexist by fashioning specific control actions. This control strategy can be beneficial for problems that can arise when there is a risk of extinction of one of the species and human intervention must be planned. One natural and well-established theory for describing systems

obeying energy balance laws is the port-Hamiltonian modeling, an extension of classical Hamiltonian mechanics to systems endowed with control and observation. The LV model can be formally represented as a non-linear mechanical oscillator employing the canonical equations of Hamilton. This special mathematical structure aids planning and designing efficient control actions. The proposed strategy employs a systematic procedure to efficiently plan biological control actions and bypass species extinction through asymptotic stabilisation of populations.

Keywords: Biological systems, Systems biology, Stochastic systems
Abstract: We consider the problem of quantifying the variance in the number of molecules of a species, in biochemical reactions with nonlinear reaction rates. We address this problem for a particular configuration where a species is formed with bursts, with a nonlinear rate that depends on another spontaneously formed species. By making use of an appropriately formulated expansion based on the Newton series, in conjunction with spectral properties of the master equation, we derive an analytical expression that provides a hard bound for the variance. We also show that this bound is exact when the propensities are linear. Furthermore, numerical simulations demonstrate that this is very close to the actual variance.

Keywords: Biological systems, Control applications, Robotics
Abstract: This paper entails the application of the energy shaping methodology to control a flexible, elastic Cosserat rod model. Recent interest in such continuum models stems from applications in soft robotics, and from the growing recognition of the role of mechanics and embodiment in biological control strategies: octopuses are often regarded as iconic examples of this interplay. The dynamics of the Cosserat rod, here modeling a single octopus arm, are treated as a Hamiltonian system and the internal muscle actuators are modeled as distributed forces and couples. The proposed energy shaping control design procedure involves two steps: (1) a potential energy is designed such that its minimizer is the desired equilibrium configuration; (2) an energy shaping control law is implemented to reach the desired equilibrium. By interpreting the controlled Hamiltonian as a Lyapunov function, asymptotic stability of the equilibrium configuration is deduced. The energy shaping control law is shown to require only the deformations of the equilibrium configuration. A forward-backward algorithm is proposed to compute these deformations in an online iterative manner. The overall control design methodology is implemented and demonstrated in a dynamic simulation environment. Results of several bio-inspired numerical experiments involving the control of octopus arms are reported.

Keywords: Automotive control, Observers for nonlinear systems, Time-varying systems
Abstract: This paper is dedicated to the powered two-wheeled vehicle (PTWV) lateral dynamics estimation. Differently from common unknown input observer (UIO) approaches reported in the literature, which considers constant output matrix and exact premise variables, this work takes into account the real measurement provided in the body-fixed frame. This consideration leads to a nonlinear parameter-dependent output equation with unmeasurable premise variables in the UIO design. The observer convergence and stability study are established by considering a quadratic Lyapunov function associated with the Input to State Stability (ISS) to guaranty boundedness of the state estimation errors. Sufficient conditions are given in terms of linear matrix inequalities (LMIs). Finally, the performances and applicability of the proposed approach are evaluated by co-simulation using BikeSim high fidelity motorcycle simulator.

Keywords: Linear parameter-varying systems, Differential-algebraic systems, Observers for Linear systems
Abstract: The main contribution of this paper is a H-infinity observer design for a new class of general singular Nonlinear Parameter-varying system in the presence of disturbances and Lipschitz nonlinearity. In specific, this observer tackles the impact of disturbance on estimation error thanks to the H-infinity norm, while the robust parameter-dependent stability of estimation dynamics helps to widen the feasible region of LMI solution under the Lipschitz constraint. Finally, a numerical example with the gridding solution is illustrated to highlight the proposed design.

Keywords: Linear parameter-varying systems, LMIs, Robust control
Abstract: This paper shows that, as long as continuous-time linear parameter-varying (LPV) systems are concerned, quadratic-stability-based gain-scheduled state-feedback controller synthesis offers no advantage over quadratic-stability-based fixed (parameter-independent) state-feedback controller synthesis in typical control performance specifications. We derive this counterintuitive result by properly extending the previous results on the robust versions of Finsler's lemma and the elimination lemma. We also show that this counterintuitive result is continuous-time LPV system specific, and in the discrete-time LPV system case quadratic-stability-based gain-scheduled state-feedback controller synthesis does bring improvement. These results give a proper warning about the effectiveness of the quadratic-stability-based gain-scheduled state-feedback controller synthesis.

Keywords: Time-varying systems, Optimal control
Abstract: An identification-free control design strategy for discrete-time linear time-varying systems with unknown dynamics is introduced. The closed-loop system (under state feedback) is parametrised with data-dependent matrices obtained from an ensemble of input-state trajectories collected offline. This data-driven system representation is used to classify control laws yielding trajectories which satisfy a certain bound and to solve the linear quadratic regulator problem - both using data-dependent linear matrix inequalities only. The results are illustrated by means of a numerical example.

Keywords: Time-varying systems, Stability of linear systems, Observers for Linear systems
Abstract: Exponential dichotomies play a central role in stability theory for dynamical systems. They allow to split the state space into two subspaces, where all trajectories in one subspace decay whereas all trajectories in the other subspace grow, uniformly and exponentially. This paper studies uniform detectability and observability notions for linear time varying systems, which admit an exponential dichotomy. The main contributions are necessary and sufficient detectability conditions for this class of systems.

Keywords: Identification
Abstract: In this paper, a recursive identification approach to single-input single-output linear time varying (LTV) systems when both the output and the input measurements are corrupted by bounded noise is considered. First, the problem is formulated in terms of errors-in-variables identification in presence of bounded noise. Then, a linear programming based algorithm for online computation of tight bounds on the parameters of the LTV system is proposed. Two simulation examples are presented in order to show the effectiveness of the proposed approach.

Keywords: LMIs, Linear parameter-varying systems, Uncertain systems
Abstract: This paper considers the problem of H infinity norm guaranteed cost computation for linear time-invariant polytopic systems, in both the continuous-time and discrete-time cases. First, a generalized problem is proposed that includes both the continuous-time and discrete-time problems as special cases. A novel description of polytopic uncertainties is then derived and used to develop a relaxation approach based on the S-procedure to lift the uncertainties. This yields a linear matrix inequality (LMI) approach to compute H infinity norm guaranteed cost by incorporating slack variables and allowing the use of a parameter-dependent Lyapunov function. Numerical examples demonstrate that the proposed conditions can provide less conservative results than the ones obtained by the previous methods from the literature.

Keywords: Robust control, Linear parameter-varying systems, LMIs
Abstract: Joint synthesis of dynamic state feedback is considered together with dynamic disturbance feedforward. First a novel parameter transformation is introduced to derive a new LMI condition for synthesis in the case of LTI systems. This condition forms the basis of a new synthesis method, which can easily be specialized to combination of static or dynamic sate feedback with static or dynamic disturbance feedforward. Moreover, it can also be used to synthesize LTI or scheduled controllers for systems that depend on uncertain time-varying parameters, some of which are not measurable online.

Keywords: Optimal control, Constrained control, Time-varying systems
Abstract: This work proposes a way to time-sparsify predesigned stabilizing feedback controls. For this purpose, a finite-time stabilizing sliding-mode feedback control law is considered. For the finite-time stabilizing controller, an on-off switching signal is designed to optimally time-sparsify the feedback control signals. Due to the non-Lipschitz nature of the sliding-mode controller, this requires the use of a non-smooth Pontryagin Maximum Principle. Numerical experiments are presented to verify the theoretical results and illustrate the advantages of the proposed ideas.

Keywords: Variable-structure/sliding-mode control, Robust control, Distributed parameter systems
Abstract: The present work extends the integral sliding mode control approach to the boundary control of systems described by an uncertain heat equation. The proposed controller entirely skips the reaching phase and thus ensures the robustness of the feedback loop to a certain class of external disturbances for all times. A formal stability analysis as well as a tutorial example and simulation results demonstrate the applicability and effectiveness of the proposed approach.

Keywords: Variable-structure/sliding-mode control, Lyapunov methods
Abstract: This paper studies a family of second-order homogeneous state-feedback controllers, which includes the well-known twisting algorithm as a special case. Upper bounds for the closed loop's convergence time are proposed that may be computed analytically for any values of the positive controller parameters. Numerical comparisons show that the bound approximates the actual convergence time to within a factor of two over a large parameter range.

Keywords: Variable-structure/sliding-mode control, Observers for nonlinear systems, Filtering
Abstract: The proposed new discretization of homogeneous filtering differentiators removes the chattering of outputs and improves the differentiation accuracy in the absence of noises, while preserving the optimal accuracy asymptotics and filtering capabilities in their presence. Numeric experiments illustrate the theoretical results for low sampling rates and for very large noises.

Keywords: Variable-structure/sliding-mode control, Lyapunov methods
Abstract: This contribution presents a novel perspective on backstepping control design and sliding mode control for second order systems. It is shown how discontinuous control laws can be induced by suitable choices of control Lyapunov functions during the backstepping procedure. The advantages of this methodology are underlined through the design of a class of robust adaptive control laws that are capable to compensate for parametric uncertainties and unknown bounded disturbances. Simulation results are presented to validate the designed control law.

Keywords: Chaotic systems, Robust adaptive control, Variable-structure/sliding-mode control
Abstract: A self-tuning fast terminal sliding model control approach is proposed in this paper for uncertain chaotic systems with unknown nonlinear functions and external disturbances. The proposed approach was derived using a sliding manifold with bipolar sigmoid function and adjustable gains to ensure finite time convergence, reachability and alleviate chattering without the requirement for prior knowledge about the upper bounds of the external disturbances. The finite time convergence of the proposed approach was established using the Lyapunov theory. Performance analysis was carried over using a Genesio-Tesi system subject to time-varying disturbances and bounded uncertainties. The numerical results were further compared to those obtained with an existing approach. Theoretical analysis and simulation results showed that faster convergence and higher-precision tracking performance were obtained with the proposed approach.

Keywords: Algebraic/geometric methods, Lyapunov methods, Mechatronics
Abstract: This paper proposes a novel framework to design a passivity based sliding mode controller for mechanical systems described by simple port-Hamiltonian systems. For this class of systems, passivity based control is often used to design a stabilizing controller which employs a physical energy of the plant system as a Lyapunov function candidate. This paper proves that there exist a special class of passivity based controllers which coincide with sliding mode ones. This approach enables us to obtain sliding mode control systems with explicit energy based Lyapunov functions. The proposed approach requires a kind of matching condition under which the two control schemes coincide with each other. How to relax the condition is also discussed. Furthermore, a numerical example demonstrates how the proposed method works.

Keywords: Agents-based systems, Cooperative control, Decentralized control
Abstract: This paper addresses the problem of bearing-only formation control in d~(dgeq 2)-dimensional space by exploring persistence of excitation (PE) of the desired bearing reference. By defining a desired formation that is bearing PE, distributed bearing-only control laws are proposed, which guarantee exponential stabilization of the desired formation only up to a translation vector. The key outcome of this approach relies in exploiting the bearing PE to significantly relax the conditions imposed on the graph topology to ensure exponential stabilization, when compared to the bearing rigidity conditions, and to remove the scale ambiguity introduced by bearing vectors. Simulation results are provided to illustrate the performance of the proposed control method.

Keywords: Autonomous robots, Cooperative control, Distributed control
Abstract: This paper investigates a distributed formation control problem for networked robots, with the global objective of achieving predefined time-varying formations in an environment with obstacles. A novel fixed-time behavioral approach is proposed to tackle the problem, where a global formation task is divided into two local prioritized subtasks, and each of them leads to a desired velocity that can achieve the individual task in a fixed time. Then, two desired velocities are combined via the framework of the null-space-based behavioral projection, leading to a desired merged velocity that guarantees the fixed-time convergence of task errors. Finally, the effectiveness of the proposed control method is demonstrated by simulation results.

Keywords: Autonomous systems, Cooperative control, Distributed control
Abstract: Distributed formation control for leader-follower multi-agent systems under prescribed performance guarantees is addressed in this paper. Leader-follower is meant in the sense that a group of agents with external inputs are selected as leaders in order to drive the group of followers in a way that the entire system can achieve the target relative position-based formation within certain prescribed performance transient bounds. In previous work, we have proposed a distributed control law for tree graphs to achieve consensus within certain prescribed transient performance when the decay rate of the performance functions is within a sufficient bound. In this paper, we further discuss the general graphs with cycles. Some necessary conditions on the graph topology are proposed in order to achieve the target formation while satisfying the prescribed performance bounds. We also discuss the roles of the cycles for the convergence benefits in this leader-follower framework. Finally, we illustrate the results with the simulation examples.

Keywords: Cooperative control, Robust control
Abstract: Train coordination technology in moving block signaling (MBS) systems has a huge potential in maximizing line utilization and railways safe operation. However, the realization of reliable cooperative control is a nontrivial task, facing challenges such as environmental uncertainties, unpredictable and time-varying disturbances. This paper investigates the robust cooperative control problem of networked homogeneous trains with physically connected carriages using the cooperative control theories for Negative Imaginary (NI) systems. The coupling between trains within the overall system is described by a network topology and a local robust Strictly Negative Imaginary (SNI) controller is designed to track a prescribed reference and maintain a pre-defined formation. Numerical simulations are provided to demonstrate the effectiveness of the proposed controller.

Keywords: Distributed control, Iterative learning control, Stability of nonlinear systems
Abstract: In this paper we consider the distributed leader-follower formation tracking problem of unknown nonlinear non-affine discrete-time repetitive multi-agent systems. The leader agent only communicates information to a subset of the follower agents and the follower agent exchanges information only with its neighbors in a directed graph. With the dynamic linearization technique in the iteration domain, a systematic way is provided for constructing a distributed formation control law, which is independent of the physical model of the multi-agent system. A distributed iterative learning control approach is designed for formation tracking using only the local measurements. The convergence of the proposed scheme is rigorously established for the controlled multi-agent system in the case of iteration-varying topologies. An illustrative example is applied to demonstrate the effectiveness of the proposed scheme.

Keywords: Distributed control, Cooperative control, Autonomous systems
Abstract: In this letter, we investigate the formation control problem of mobile robots moving in the plane where, instead of assuming robots to be simple points, each robot is assumed to have the form of a disk with equal radius. Based on interior angle measurements of the neighboring robots' disk, which can be obtained from low-cost vision sensors, we propose a gradient-based distributed control law and show the exponential convergence property of the associated error system. By construction, the proposed control law has the appealing property of ensuring collision avoidance between neighboring robots. We also present simulation results for a team of four circular mobile robots forming a rectangular shape.

Keywords: Intelligent systems, Distributed control, Predictive control for linear systems
Abstract: This work develops a novel strategy for splitting and merging of agents travelling in formation. The method converts the formation control problem into an optimization problem, which is solved among the agents in a distributed fashion. The proposed control strategy is one type of Distributed Model Predictive Control (DMPC) which allows the system to cope with disturbances and dynamic environments. A modified Alternating Direction Method of Multipliers (ADMM) is designed to solve the trajectory optimization problem and achieve formation scaling. Furthermore, a mechanism is designed to implement path homotopy in splitting and merging of the formation, which examines the H-signature of the generated trajectories. Simulation shows that, by using the proposed method, the formation is able to automatically resize and dynamically split to better avoid obstacles, even in the case of losing communication among agents. Upon splitting the newly formed groups proceed and merge again when it becomes possible.

Keywords: Optimal control, Agents-based systems
Abstract: Lack of availability of adequate bandwidth for simultaneous communication between a large number of agents and the central processing unit motivates us to study a multiagent system employing time multiplexed control. Achieving a formation under such time-multiplexing constraints is posed as a discrete constrained optimal control problem. Employing the discrete Pontryagin Maximum Principle (DMP) we obtain first order necessary conditions to be satisfied by an optimal control law, which tackles both problems of formation control and time multiplexing simultaneously. The information structure of relative states is embedded into the problem using a graph theoretic framework. The necessary conditions appear in the form of a two-point boundary value problem and this is solved using a multiple shooting method. The results are then validated through numerical experiments for various cases.

Keywords: Autonomous vehicles, Agents-based systems, Game theory
Abstract: Cooperatively planning for multiple agents has been proposed as a promising method for strategic and motion planning for automated vehicles. By taking into account the intent of every agent, the ego agent can incorporate future interactions with human-driven vehicles into its planning. The problem is often formulated as a multi-agent game and solved using iterative algorithms operating on a discretized action or state space. Even if converging to a Nash equilibrium, the result will often be only sub-optimal. In this paper, we define a linear differential game for a set of interacting agents and solve it to optimality using mixed-integer programming. A disjunctive formulation of the orientation allows us to formulate linear constraints to prevent agent-to-agent collision while preserving the non-holonomic motion properties of the vehicle model. Soft constraints account for prediction errors. We then define a joint cost function, where a cooperation factor can adapt between altruistic, cooperative, and egoistic behavior. We study the influence of the cooperation factor to solve scenarios, where interaction between the agents is necessary to solve them successfully. The approach is then evaluated in a racing scenario, where we show the applicability of the formulation in a closed-loop receding horizon replanning fashion. By accounting for inaccuracies in the cooperative assumption and the actual behavior, we can indeed successfully plan an optimal control strategy interacting closely with other agents.

Keywords: Autonomous vehicles, Automotive systems, Robotics
Abstract: A major aspect of motion planning is the use of sampling-based algorithms. Sampling-based methods are primarily used to generate a feasible collision-free path for agents in an environment known a-priori. A recently proposed motion planning algorithm, termed as ’Generalized Shape Expansion’ (GSE) algorithm, is a promising option in this class of algorithm. Extensive numerical studies have suggested that the GSE outperforms several seminal algorithms in literature in terms of computational time. However, so far no guarantee of probabilistic completeness of the GSE has been presented in literature. To this end, this paper elaborates a detailed mathematical analysis of GSE, providing upper bounds on the probability of failure of the GSE algorithm. A numerical example is presented to illustrate the proof. Simulation studies are presented to compare it with prominent algorithms in the literature, particularly in terms of number of iterations to reach a feasible path.

Keywords: Autonomous vehicles, Nonholonomic systems, Optimal control
Abstract: We address the problem of optimal path planning for a Dubins-type nonholonomic vehicle in the presence of obstacles. Most current approaches are either split hierarchically into global path planning and local collision avoidance, or neglect some of the ambient geometry by assuming the car is a point mass. We present a Hamilton-Jacobi formulation of the problem that resolves time-optimal paths and considers the geometry of the vehicle.

Keywords: Autonomous vehicles, Uncertain systems, Predictive control for nonlinear systems
Abstract: Motion planning and control algorithms for autonomous vehicles need to be safe, and consider future movements of other road users to ensure collision-free trajectories. In this paper, we present a control scheme based on Model Predictive Control (MPC) with robust constraint satisfaction where the constraint uncertainty, stemming from the road users' behavior, is multimodal. The method combines ideas from tube-based and scenario-based MPC strategies in order to approximate the expected cost and to guarantee robust state and input constraint satisfaction. In particular, we design a feedback policy that is a function of the disturbance mode and allows the controller to take less conservative actions. The effectiveness of the proposed approach is illustrated through two numerical simulations, where we compare it against a standard robust MPC formulation.

Keywords: Robotics, Autonomous vehicles, Autonomous robots
Abstract: We propose a novel receding horizon planner for an autonomous surface vehicle (ASV) performing path planning in urban waterways. Feasible paths are found by repeatedly generating and searching a graph reflecting the obstacles observed in the sensor field-of-view. We also propose a novel method for multi-objective motion planning over the graph by leveraging the paradigm of lexicographic optimization and applying it to graph search within our receding horizon planner. The competing resources of interest are penalized hierarchically during the search. Higher-ranked resources cause a robot to incur non-negative costs over the paths traveled, which are occasionally zero-valued. The framework is intended to capture problems in which a robot must manage resources such as risk of collision. This leaves freedom for tie-breaking with respect to lower-priority resources; at the bottom of the hierarchy is a strictly positive quantity consumed by the robot, such as distance traveled, energy expended or time elapsed. We conduct experiments in both simulated and real-world environments to validate the proposed planner and demonstrate its capability for enabling ASV navigation in complex environments.

Keywords: Robotics, Machine learning, Neural networks
Abstract: This work proposes a hybrid control methodology to achieve full body collision avoidance in anthropomorphic robot manipulators. The proposal improves classical motion planning algorithms by introducing a Deep Reinforcement Learning (DRL) approach trained ad hoc for performing obstacle avoidance, while achieving a reaching task in the operative space. More specifically, a switching mechanism is enabled whenever a condition of proximity to the obstacles is met, thus conferring to the dual-mode architecture a self-configuring capability in order to cope with objects unexpectedly invading the workspace. The proposal has been finally tested relying on a realistic robot manipulator simulated in a V-REP environment.

Keywords: Machine learning, Neural networks, Adaptive control
Abstract: We present an on-line approach for coverage path planning in 2D grid environments based on reinforcement learning. We used actor-critic architecture with convolutional layers to learn an agent's policy from simulated limited-range sensor observations. We experimented with different reward functions and network architectures to get a minimal repetition rate. Our results show that model generalizes well to unseen environments with complex geometry and dynamic obstacles and demonstrates the ability to learn some optimal trajectory patterns like circular and boustrophedon motion. An approach may as well be suitable for a multi-agent setting with minor adjustments, as shown by our simulations.

Keywords: Switched systems, Optimal control, Autonomous vehicles
Abstract: We consider a finite element approximation of the Hamilton-Jacobi-Bellman equation for the optimal control of switched systems. In particular, we show that the obtained finite dimensional problem belongs to a special class of problems that we already studied in a previous work. In that work, we also presented a simple and efficient solution algorithm. As an application, we present the problem of generating parking maneuvers for self-driving vehicles. The vehicle is described by a switched system. Each change between forward and backward motion is associated to a switching cost. This added cost penalizes the maneuvers with a larger number of direction changes and allows obtaining simpler and more human-like trajectories.

Keywords: Robotics, Estimation, Stochastic systems
Abstract: Estimating the state of a stochastic differential equation (SDE) evolving in a Stiefel manifold occurs in many applications in science and engineering. This problem has been handled by particle filtering. However, many existing schemes share common shortcomings: estimated states fail to satisfy geometric constraints in the sampling step and the conventional particle filter suffers from particle depletion in the resampling step. Here we overcome these issues by managing the geometry with a numerical Ito-Cayley scheme and ensuring particle diversity with optimal transport. We give simulations to illustrate the new algorithm.

Keywords: Robotics, Estimation, Stochastic systems
Abstract: The Cramer-Rao bound (CRB) is a fundamental limit to estimator performance. It has been extended to parameters in manifolds in different ways in two literatures; statistics and signal processing. We review those extensions here and then complement them by providing a new formula for the Riemannian CRB. We then turn to parameter estimation in SO(3) and provide a new approach which is applied to the Wahba problem and compared with a recently developed alternative.

Keywords: Robotics, Machine learning, Cooperative control
Abstract: Multi-robot learning has been extensively studied recently. Developing provably-correct algorithms for learning decentralized control policies remains challenging. In this paper, we propose a sample-efficient multi-robot learning method based on guided policy search to learn decentralized swarm control policies. The proposed method uses distributed trajectory optimization to provide guiding trajectory samples for policy training. In turn, the learned policy is exploited to update trajectory optimization results so that the guiding trajectories are reproducible by the current policy. A learning algorithm is designed to alternate between distributed trajectory optimization and policy optimization, which eventually converges to the solution with good long-term performance. We demonstrate the effectiveness of our method in a multi-robot rendezvous problem. The simulation results in a robot simulator show that our method efficiently learn decentralized control policy with substantially less training samples.

Keywords: Robotics, Machine learning, Neural networks
Abstract: In this work we present a novel extension of soft actor critic, a state of the art deep reinforcement algorithm. Our method allows us to combine traditional controllers with learned neural network policies. This combination allows us to leverage both our own domain knowledge and some of the advantages of model free reinforcement learning. We demonstrate our algorithm by combining a hand designed linear quadratic regulator with a learned controller for the acrobot problem. We show that our technique outperforms other state of the art reinforcement learning algorithms in this setting.

Keywords: Robotics, Emerging control applications, Feedback linearization
Abstract: We introduce here a novel under-actuated mechanical system motivated by recent advances in soft robotics. We derive its governing equations, discuss its properties, and consider a solution for the stabilization of its unstable equilibrium. The results we propose here are intended as a first step towards dealing with the much more challenging general problem of controlling full fledged soft robots subject to non negligible external forces and operating at high accelerations.

Keywords: Robotics, Nonlinear systems identification, Feedback linearization
Abstract: Many position-controlled robots are being used in research and industry in the world, but many tasks require torque control instead of position control, in order to exert specific forces in the environment. This is often called the admittance control problem. In this paper, we present a solution for position-controlled robots by estimating their hidden internal control law using Neural Networks and mitigating the fitting errors with an integral term in the control law. Compared to classical approaches, we no longer consider that the control law is decoupled between motors but it can be highly sophisticated and nonlinear. We show our results in simulation by performing torque tracking and force-position task control.

Keywords: Robotics, Optimal control
Abstract: We present a complete synthesis method for time-optimal rest-to-rest motions of an elastic joint system with bounded torque input. An equivalence with the two-body problem in classical mechanics is highlighted, allowing to introduce a change of coordinates that reduces the problem to a pair of decoupled one-body problems. In place of the original coupled fourth-order dynamics, the motion of two equivalent masses has to be synchronized in separate phase spaces. The solution is provided in closed form by following purely geometric arguments, and verifies the standard optimality conditions. The obtained control is a bang-bang policy with either one or three switchings, depending on the dynamic parameters and the required displacement. One-switching solutions are called natural motions for the system: given a set of dynamic parameters, they cover the displacement space in a sparse way. Natural motions are the only instances when minimum-time solutions for the elastic and the equivalent rigid joint system match, whereas the rigid system is faster for all other optimal rest-to-rest motions.

Keywords: Robotics, Optimization, Optimal control
Abstract: Trajectory optimization is an important tool for control and planning of complex, underactuated robots, and has shown impressive results in real world robotic tasks. However, in applications where the cost function to be optimized is non-smooth, modern trajectory optimization methods have extremely slow convergence. In this work, we present TRON, an iterative solver that can be used for efficient trajectory optimization in applications with non-smooth cost functions that are composed of smooth components. TRON achieves this by exploiting the structure of the objective to adaptively smooth the cost function, resulting in a sequence of objectives that can be efficiently optimized. TRON is provably guaranteed to converge to the global optimum of the non-smooth convex cost function when the dynamics are linear, and to a stationary point when the dynamics are nonlinear. Empirically, we show that TRON has faster convergence and lower final costs when compared to other trajectory optimization methods on a range of simulated tasks including collision-free motion planning for a mobile robot, sparse optimal control for surgical needle, and a satellite rendezvous problem.

Keywords: Observers for nonlinear systems, Distributed parameter systems, Estimation
Abstract: The design problem of a high-gain observer is considered for some 2x2 and 3x3 semilinear reaction-diffusion systems, with possibly distinct diffusivities, and considering distributed measurement of part of the state. Due to limitations imposed by the parabolic operator, for the design of such an observer, an infinite-dimensional state transformation is first applied to map the system into a more suitable set of partial differential equations. The observer is then proposed including output correction terms and also spatial derivatives of the output of order depending on the number of distinct diffusivities. It ensures arbitrarily fast state estimation in the sup-norm. The result is illustrated with a simulated example of a Lotka-Volterra system.

Keywords: Observers for nonlinear systems, Estimation, Lyapunov methods
Abstract: In this paper, alternative adaptive observers are developed for nonlinear systems to achieve state observation and parameter estimation of nonlinear systems simultaneously. The proposed observers are derived from the perspective of adaptive parameter estimation method, which leads to the reduced-order observers to deal with partially unknown system states and unknown parameters. To be specific, the nonlinear parametric function of unknown states to be identified is first transformed into a cascade form, which is linearly independent of unknown constant parameters. This transformation is achieved by finding an unmeasurable injective mapping function. Then, the functions related to measurable states are injected into a set of low-pass filters to derive the relationship between the mapping function and unknown parameters. In this line, the observer design problem is transformed into an equivalent parameter estimation problem. Consequently, we further exploit a recently proposed parameter estimation method that differs from the classical gradient descent algorithm to estimate the mapping function and unknown constant parameters. Finally, the unknown system states can be reconstructed by inverting this mapping function. A simulation example of DC-DC converter illustrates the effectiveness of proposed method.

Keywords: Observers for nonlinear systems, Estimation, Sensor fusion
Abstract: This paper unveils a novel discovery that the full relative pose of a monocular camera moving in a three dimensional space can be estimated exploiting bearing measurements of only 3 unknown source points (together with velocity measurements) without any additional knowledge if the camera translational motion is sufficiently exciting. The epipolar constraint commonly used in Computer Vision algebraic algorithms for the determination of the so-called essential matrix (all of them require at least 5 source points) is here exploited in the design of the proposed Riccati observer for pose estimation. One remarkable feature of this work is the determination of an explicit persistence of excitation condition that guarantees uniform observability and, subsequently, (local) exponential stability of the proposed observer. Convincing simulation results are provided to support the proposed approach.

Keywords: Observers for nonlinear systems, Estimation, Lyapunov methods
Abstract: This paper deals with the problem of state estimation of dynamic systems with Lipschitz nonlinearities using a new high gain observer design. The aim of this new design procedure is to reduce the value of the tuning parameter and the observer gain compared to the standard high gain observer on the one hand without solving a set of LMIs as in the LMI based observer on the other hand. Towards this end, a novel approach based on system state augmentation that transforms the original system of dimension n into a new system whose dimension is (n + j_s), where the new nonlinear function does not depend on j_s last components of the new state. A numerical example is reported to evaluate the effectiveness of the proposed observer for different values of the Lipschitz constant.

Keywords: Observers for nonlinear systems, Estimation, Kalman filtering
Abstract: Accurate localisation of unmanned aerial vehicles is vital for the next generation of automation tasks. This paper proposes a minimum energy filter for velocity-aided pose estimation on the extended special Euclidean group. The approach taken exploits the Lie-group symmetry of the problem to combine Inertial Measurement Unit (IMU) sensor output with landmark measurements into a robust and high performance state estimate. We propose an asynchronous discrete-time implementation to fuse high bandwidth IMU with low bandwidth discrete-time landmark measurements typical of real-world scenarios. The filter's performance is demonstrated by simulation.

Keywords: Observers for nonlinear systems, Lyapunov methods, Sensor fusion
Abstract: This paper presents the equivariant systems theory and observer design for second order kinematic systems on matrix Lie groups. The state of a second order kinematic system on a matrix Lie group is naturally posed on the tangent bundle of the group with the inputs lying in the tangent of the tangent bundle known as the double tangent bundle. We provide a simple parameterization of both the tangent bundle state space and the input space (the fiber space of the double tangent bundle) and then introduce a semi-direct product group and group actions onto both the state and input spaces. We show that with the proposed group actions the second order kinematics are equivariant. An equivariant lift of the kinematics onto the symmetry group is defined and used to design a nonlinear observer on the lifted state space using nonlinear constructive design techniques. A simple hovercraft simulation verifies the performance of our observer.

Keywords: Observers for nonlinear systems, Nonlinear output feedback, Stability of nonlinear systems
Abstract: A globally asymptotically stable nonlinear system cascaded by a single input single output linear system through its output has been shown to be semi-globally asymptotically stabilizable by low-and-high gain feedback of the state of the linear system if the linear system is controllable and with its invariant zeros located at the origin. Such low-and-high state feedback can be implemented by an observer. To retain a domain of attraction arbitrarily close to the domain of attraction under a given state feedback, high gain observer is employed to achieve arbitrarily fast decay of the observation errors of all states and the effect of the peaking phenomenon associated with the high observer gain is overcome by saturating the control input outside a region that contains the desired domain of attraction. In this paper, we propose a co-design of the linear low-and-high gain state feedback and the high gain observer for semi-global stabilization of such a cascaded system without resorting to saturating the control input. Moreover, our design does not rely on making all state observation errors decay to zero arbitrarily fast.

Keywords: Observers for nonlinear systems, Stability of nonlinear systems
Abstract: This paper studies the behaviour of observers for the slow states of a general singularly perturbed system - that is a singularly perturbed system which has boundary-layer solutions that do not necessarily converge to a slow manifold. The solutions of the boundary-layer system are allowed to exhibit persistent (e.g. oscillatory) steady-state behaviour which are averaged to obtain the dynamics of the approximate slow system. It is shown that if an observer has certain properties such as asymptotic stability of its error dynamics on average, then it is practically asymptotically stable for the original singularly perturbed system.

Keywords: Computational methods, Optimization, Large-scale systems
Abstract: In this paper, we propose an incremental abstraction method for dynamically over-approximating nonlinear systems in a bounded domain by solving a sequence of linear programs, resulting in a sequence of affine upper and lower hyperplanes with expanding operating regions. Although the affine abstraction problem can be solved using a single linear program, existing approaches suffer from a computation space complexity that grows exponentially with the state dimension. Thus, the motivation for incremental abstraction is to reduce the space complexity of abstraction algorithms for high-dimensional systems or systems with limited on-board resources. Specifically, we start with an operating region that is a subregion of the state space and compute a pair of affine hyperplanes that bracket the nonlinear function locally. Then, by incrementally expanding the operating region, we dynamically update the two affine hyperplanes such that we eventually yield hyperplanes that are guaranteed to over-approximate the nonlinear system over the entire domain. Finally, the effectiveness of the proposed approach is demonstrated using several numerical examples.

Keywords: Optimization algorithms, Delay systems, Agents-based systems
Abstract: This work investigates the distributed constrained optimization problem under inter-agent communication delays from the perspective of passivity. First, we propose a continuous-time algorithm for distributed constrained optimization with general convex objective functions. The asymptotic stability under general convexity is guaranteed by the phase lead compensation. The inequality constraints are handled by adopting a projection-free generalized Lagrangian, whose primal-dual gradient dynamics preserves passivity and smoothness, enabling the application of the LaSalle's invariance principle in the presence of delays. Then, we incorporate the scattering transformation into the proposed algorithm to enhance the robustness against unknown and heterogeneous communication delays. Finally, a numerical example of a matching problem is provided to illustrate the results.

Keywords: Estimation, Identification
Abstract: One of the major contributions to sparse learning has been to quantify how the correlation between the regressors affect the ability to recover a sparse parameter vector. Roughly, the inverse of the maximum correlation controls how many non-zero parameters can be exactly recovered from an under-determined system of equations. This result is of importance also in system identification where observations are noisy. Unfortunately, for such problems the regressors are highly correlated making sparse identification difficult. In this contribution we address this problem by applying a linear transformation to the regressors, selected in such a way that the correlation is reduced. The latter is achieved by formulating a constrained optimization problem which is solved using a proximal method. The method can be seen as a pre-processing step that can be used prior to any sparse estimation algorithm. Simulations are used to demonstrate the usefulness of the method.

Keywords: Optimization, Optimization algorithms
Abstract: We propose a framework to use Nesterov’s accelerated method for constrained convex optimization problems. Our approach consists of first reformulating the original problem as an unconstrained optimization problem using a continuously differentiable exact penalty function. This reformulation is based on replacing the Lagrange multipliers in the augmented Lagrangian of the original problem by Lagrange multiplier functions. The expressions of these Lagrange multiplier functions, which depend upon the gradients of the objective function and the constraints, can make the unconstrained penalty function non-convex in general even if the original problem is convex. We establish sufficient conditions on the objective function and the constraints of the original problem under which the unconstrained penalty function is convex. This enables us to use Nesterov’s accelerated gradient method for unconstrained convex optimization and achieve a guaranteed rate of convergence which is better than the state-of-the-art first-order algorithms for constrained convex optimization. Simulations illustrate our results.

Keywords: Optimization, Optimization algorithms, Lyapunov methods
Abstract: Motivated by the fact that the gradient-based optimization algorithms can be studied from the perspective of limiting ordinary differential equations (ODEs), here we derive an ODE representation of the accelerated triple momentum (TM) algorithm. For unconstrained optimization problems with strongly convex cost, the TM algorithm has a proven faster convergence rate than the Nesterov's accelerated gradient (NAG) method but with the same computational complexity. We show that similar to the NAG method, in order to accurately capture the characteristics of the TM method, we need to use a high-resolution modeling to obtain the ODE representation of the TM algorithm. We propose a Lyapunov analysis to investigate the stability and convergence behavior of the proposed high-resolution ODE representation of the TM algorithm. We compare the rate of the ODE representation of the TM method with that of the NAG method to confirm its faster convergence. Our study also leads to a tighter bound on the worst rate of convergence for the ODE model of the NAG method. In this paper, we also discuss the use of the integral quadratic constraint (IQC) method to establish an estimate on the rate of convergence of the TM algorithm. A numerical example verifies our results.

Keywords: Optimization, Stability of nonlinear systems
Abstract: This paper concerns a new class of discontinuous dynamical systems for constrained optimization. These dynamics are particularly suited to solve nonlinear, non-convex problems in closed-loop with a physical system. Such approaches using feedback controllers that emulate optimization algorithms have recently been proposed for the autonomous optimization of power systems and other infrastructures. In this paper, we consider feedback gradient flows that exploit physical input saturation with the help of anti-windup control to enforce constraints. We prove semi-global convergence of ``projected'' trajectories to first-order optimal points, i.e., of the trajectories obtained from a pointwise projection onto the feasible set. In the process, we establish properties of the directional derivative of the projection map for non-convex, prox-regular sets.

Keywords: Optimization algorithms, Stability of nonlinear systems
Abstract: In this paper, we present a novel control scheme for feedback optimization. That is, we propose a discrete-time controller that can steer a physical plant to the solution of a constrained optimization problem without numerically solving the problem. Our controller can be interpreted as a discretization of a continuous-time projected gradient flow. Compared to other schemes used for feedback optimization, such as saddle-point schemes or inexact penalty methods, our control approach combines several desirable properties: it asymptotically enforces constraints on the plant steady-state outputs, and temporary constraint violations can be easily quantified. Our scheme requires only reduced model information in the form of steady-state input-output sensitivities of the plant. Further, global convergence is guaranteed even for non-convex problems. Finally, our controller is straightforward to tune, since the step-size is the only tuning parameter.

Keywords: Computational methods, Stability of nonlinear systems, Optimization algorithms
Abstract: This paper provides a dynamical system perspective on the escape of sharp local minima in constrained optimization problems. The dynamical system view models a perturbed projected first-order optimization algorithm and translates the problem of escaping local minima in constrained optimization problems to that of escaping regions of attraction of the corresponding dynamical system. We develop the notion of biased perturbation and show that it gives a quantitative view of the notion of small regions of attraction that can be escaped. As a counterpart, we explain why the dynamics is stable in a wide region of attraction around a strongly stable equilibrium. Numerical examples are provided to illustrate the usefulness of the developed concepts.

Keywords: Stochastic systems, Robust control, LMIs
Abstract: This work involves the design of controllers to stabilize a linear stochastic system. The system contains time-invariant and time-varying stochastic parameters, which makes it difficult to ensure stability. To overcome this challenge, the system is expanded into a linear system with only the time-invariant parameter. A compression operator is used to reduce the dimension of the expanded system. Guarantee of stochastic stability of the original system reduces to that of robust stability of the expanded system. A condition for the robust stability is characterized using matrix inequalities because the expanded system can be treated as a well-known linear polytopic system. The inequalities are just cubic matrix inequalities (CMIs) of a state feedback gain for the original system and decision variables. This paper presents a technique to transform the CMIs into quadratic matrix inequalities (QMIs). Solving the QMIs derives a stabilizing controller with the feedback gain.

Keywords: Stochastic systems, Uncertain systems, Optimal control
Abstract: This study explores a finite-horizon optimal control problem of nonlinear discrete-time systems for steering a probability distribution of initial states as close as possible to a desired probability distribution of terminal states. The problem is formulated as an optimal control problem of the Mayer form, with the terminal cost given by the Wasserstein distance, which provides a metric on probability distributions. For this optimal control problem, this paper provides a necessary condition of the optimality as a variation of the minimum principle of standard optimal control problems. The motivation for exploring this optimal control problem was to provide a control-theoretic viewpoint of a machine-learning algorithm called “the normalizing flow”. The obtained necessary condition is employed for developing a simple variation of the normalizing flow approach, and a gradient descent-type numerical algorithm is also provided.

Keywords: Stochastic systems, Uncertain systems, Lyapunov methods
Abstract: We analyze stochastic differential equations and their discretizations to derive novel high probability tracking bounds for exponentially stable time varying systems which are corrupted by process noise. The bounds have an explicit dependence on the rate of convergence for the unperturbed system and the dimension of the state space. The magnitude of the stochastic deviations have a simple intuitive form, and our perturbation bounds also allow us to derive tighter high probability bounds on the tracking of reference trajectories than the state of the art. The resulting bounds can be used in analyzing many tracking control schemes.

Keywords: Stochastic systems
Abstract: This paper investigates the stability for Markov jump linear singular system.It yields that mode to mode causality and regularity are sufficient conditions. Mean square stability is analyzed using the spectral radius of a certain matrix. In addition, the equivalence between the different definitions of stability is presented. Finally, a simple example is set to check the results.

Keywords: Stochastic systems, Robust control, Learning
Abstract: We present a data-driven model predictive control scheme for chance-constrained Markovian switching systems with unknown switching probabilities. Using samples of the underlying Markov chain, ambiguity sets of transition probabilities are estimated which include the true conditional probability distributions with high probability. These sets are updated online and used to formulate a time-varying, risk-averse optimal control problem. We prove recursive feasibility of the resulting MPC scheme and show that the original chance constraints remain satisfied at every time step. Furthermore, we show that under sufficient decrease of the confidence levels, the resulting MPC scheme renders the closed-loop system mean-square stable with respect to the true-but-unknown distributions, while remaining less conservative than a fully robust approach.

Keywords: Stochastic systems, Markov processes, Lyapunov methods
Abstract: In the paper, we study the so-called p-safety of a Markov chain. We say that a state is p-safe in a state space S with respect to an unsafe set U if the process stays in the state space and hits the set U with the probability less than p. We show several ways of computing p-safety: by means of the Dirichlet problem, the evolution equation, the barrier certificates, and the Martin kernel. The set of barrier certificates forms a cone. We show how to generate barrier certificates from the set of extreme points of a cone base.

Keywords: Stochastic systems, Identification, Stability of linear systems
Abstract: Building on a recent paper by Georgiou and Lindquist [1] on the problem of rank deficiency of spectral densities and hidden dynamical relations after sampling of continuous-time stochastic processes, this paper is devoted to understanding related questions of feedback and Granger causality that affect stability properties. This then naturally connects to CARMA identification, where we remark on certain oversights in the literature.

Keywords: Stochastic systems
Abstract: In this note we compare two notions of stochastic relative degree. Specifically, we consider nonlinear stochastic systems defined by the same stochastic differential equation and interpreted in either Ito's or Stratonovich's sense. We then recall the Ito stochastic relative degree and we introduce the concept of Stratonovich stochastic relative degree and Stratonovich normal form. We show, by means of examples, that the stochastic relative degrees arising from the two different interpretations of the same stochastic differential equations are, in general, different. We finally point out that this discrepancy can be eliminated through conversion formulas between Ito and Stratonovich integrals.

Keywords: Estimation, Agents-based systems, Kalman filtering
Abstract: Large-scale agent systems have foreseeable applications in the near future. Estimating their macroscopic density is critical for many density-based optimization and control tasks, such as sensor deployment and city traffic scheduling. In this paper, we study the problem of estimating their dynamically varying probability density, given the agents' individual dynamics (which can be nonlinear and time-varying) and their states observed in real-time. The density evolution is shown to satisfy a linear partial differential equation uniquely determined by the agents' dynamics. We present a density filter which takes advantage of the system dynamics to gradually improve its estimation and is scalable to the agents' population. Specifically, we use kernel density estimators (KDE) to construct a noisy measurement and show that, when the agents' population is large, the measurement noise is approximately ``Gaussian''. With this important property, infinite-dimensional Kalman filters are used to design density filters. It turns out that the covariance of measurement noise depends on the true density. This state-dependence makes it necessary to approximate the covariance in the associated operator Riccati equation, rendering the density filter suboptimal. The notion of input-to-state stability is used to prove that the performance of the suboptimal density filter remains close to the optimal one. Simulation results suggest that the proposed density filter is able to quickly recognize the underlying modes of the unknown density and automatically ignore outliers, and is robust to different choices of kernel bandwidth of KDE.

Keywords: Estimation, Control over communications, Stochastic systems
Abstract: We analyze the convergence of distributed consensus+ innovations parameter estimation algorithms over uncertain networks with communication noises. The linear observation of the unknown parameter by each agent, the underlying noisy communication network, and the noises therein are respectively characterized by a sequence of randomly time-varying observation matrices, random digraphs, and random variables. At each time step, every agent updates its estimation upon its measurement and interaction with its neighbors iteratively. By martingale convergence, algebraic graph and stochastic time-varying system theories, we prove that the algorithm gains can be designed properly such that all agents’estimates converge to the real parameter in mean square if the observation matrices and communication graphs satisfy the stochastic spatio-temporal persistence of excitation condition.

Keywords: Estimation, Genetic regulatory systems, Linear systems
Abstract: This paper addresses the problem of reachable set estimation for switched genetic regulatory networks with mixed delays and bounded disturbances. A delay-dependent sufficient condition is investigated to guarantee that the reachable set of genetic regulatory networks under consideration is contained within a Cartesian product of two polytopes or spheres. The sufficient condition involves only some simple inequalities, which can be easily verified by using the usual tool software. A numerical example is given to present that the proposed method is effective. Compared with the Lyapunov--Krasovskii functional method that has been used in many literature, the proposed method have two advantages: (i) No Lyapunov--Krasovskii functional is required; and (ii) Less computational complexity is involved.

Keywords: Estimation, Sensor networks, LMIs
Abstract: In this paper, an estimation problem for the sensor networks is studied in the frameworks of anisotropy-based theory. The considered system is described by linear discrete time-varying model with several sensors on finite horizon. Each sensor operates its own measurements and measurements given from some others. Any sensor could fail in random time instant. The external disturbance is assumed to be coloured sequence with given level of anisotropy. Dynamics of combined error and extended state system is governed by multiplicative noise system. Anisotropic norm boundedness for error system is guaranteed by applying of anisotropy-based bounded real lemma for multiplicative noise system. The solution of considered problem is reduced to convex optimisation problem.

Keywords: Estimation, Stochastic systems, Networked control systems
Abstract: This paper focuses on the state estimation over unreliable communication channels, where the packet dropouts occur from the sensor side to the filter, for discrete-time systems with both power bounded disturbances and white Gaussian noises. A cascaded estimation scheme with recovered robustness is proposed, driven by the residual signal related to the modeling mismatch. Through the adjoint operator, the estimation gains are explicitly characterized by two modified algebraic Riccati equations, together with a complete and rigorous stability analysis in the mean square sense. An example is included to validate the presented design method.

Keywords: Identification, Network analysis and control, Closed-loop identification
Abstract: This work focuses on the identifiability of dynamical networks with partial excitation and measurement: a set of nodes are interconnected by unknown transfer functions according to a known topology, some nodes are subject to external excitation, and some nodes are measured. The goal is to determine which transfer functions in the network can be recovered based on the input-output data collected from the excited and measured nodes.

We propose a local version of network identifiability, representing the ability to recover transfer functions which are approximately known, or to recover them up to a discrete ambiguity. We show that local identifiability is a generic property, establish a necessary and sufficient condition in terms of matrix generic ranks, and exploit this condition to develop an algorithm determining, with probability 1, which transfer functions are locally identifiable. Our implementation presents the results graphically, and is publicly available.

Keywords: Identification, Network analysis and control, Learning
Abstract: In this paper, we consider the problem of identifying one system (module) embedded in a dynamic network that is disturbed by colored process noise sources, which can possibly be correlated. To achieve this using the direct method for single module identification, we need to formulate a Multi-Input-Multi-Output (MIMO) estimation problem which requires model order selection step for each module in the setup and estimation of large number of parameters. This results in a larger variance in the estimates and an increase in computation complexity. Therefore, we extend the Empirical Bayes Direct Method, which handles the above mentioned problems for a Multi-Input-Single-Output (MISO) setup to a MIMO setting by suitably modifying the framework. We keep a parametric model for the desired target module and model the impulse response of all the other modules as independent zero mean Gaussian process governed by a first-order stable spline kernel. The parameters of the target module are obtained by maximizing the marginal likelihood of the output using the Empirical Bayes (EB) approach. To solve this, we use the Expectation Maximization (EM) algorithm which offers computational advantages. Numerical simulation illustrate the advantages of the developed method over existing classical methods.

Keywords: Identification, Network analysis and control, Linear systems
Abstract: For consistent or minimum variance estimation of a single module in a dynamic network, a predictor model has to be chosen with selected inputs and outputs, composed of a selection of measured node signals and possibly external excitation signals. The predictor model has to be chosen in such a way that consistent estimation of the target module is possible, under the condition that we have data-informativity for the considered predictor model set. Consistent and minimum variance estimation of target modules is typically obtained if we follow a direct method of identification and predictor model selection, characterized by the property that measured node signals are the prime predictor input signals. In this paper the concept of data-informativity for network models will be formalized, and for the direct method the required data-informativity conditions will be specified in terms of path-based conditions on the graph of the network model, guaranteeing data-informativity in a generic sense, i.e. independent on numerical values of the network transfer functions concerned.

Keywords: Distributed control, Agents-based systems, Linear parameter-varying systems
Abstract: This paper considers formation control for heterogeneous networks of locally controlled linear time-invariant (LTI) and linear parameter-varying (LPV) agents using a decoupled control architecture. For such networks, bounds on the agents' peak tracking error are derived based on the induced L₂ to L_∞ system norm. Furthermore, we propose linear matrix inequality (LMI) conditions to synthesize local state-feedback controllers that minimize the bound on the tracking error and additionally demonstrate that applying H_∞ synthesis techniques leads to a comparable performance. Finally, the approach of this paper is illustrated for LTI and LPV agents using two examples.

Keywords: Distributed control, Iterative learning control, Predictive control for linear systems
Abstract: This paper presents a distributed learning model predictive control (DLMPC) scheme for distributed linear time invariant systems with coupled dynamics and state constraints. The proposed solution method is based on an online distributed optimization scheme with nearest-neighbor communication. If the control task is iterative and data from previous feasible iter- ations are available, local data are exploited by the subsystems in order to construct the local terminal set and terminal cost, which guarantee recursive feasibility and asymptotic stability, as well as performance improvement over iterations. In case a first feasible trajectory is difficult to obtain, or the task is non-iterative, we further propose an algorithm that efficiently explores the state-space and generates the data required for the construction of the terminal cost and terminal constraint in the MPC problem in a safe and distributed way. In contrast to other distributed MPC schemes which use structured positive invari- ant sets, the proposed approach involves a control invariant set as the terminal set, on which we do not impose any distributed structure. The proposed iterative scheme converges to the global optimal solution of the underlying infinite horizon optimal control problem under mild conditions. Numerical experiments demonstrate the effectiveness of the proposed DLMPC scheme.

Keywords: Distributed control, Linear systems, Networked control systems
Abstract: In this paper, we consider the leader-following consensus problem of a class of linear multi-agent systems (MASs) with nonidentical random packet loss. The network topology among all agents is described as a directed graph and the packet loss across each communication channel in the network is modeled by the Bernoulli process. A distributed protocol is proposed such that the L₁-consensus of the MASs can be achieved. Moreover, the packet loss of the communication channels is allowed to be nonidentical, and the network topology is only required to be a directed graph containing a spanning tree. Finally, a simulation example is used to illustrate the derived results.

Keywords: Distributed control, Optimization, Optimization algorithms
Abstract: In this paper we develop a multi-agent distributed algorithm to solve a quadratic programming problem with linear time-varying constraints. In more detail, we first solve the frozen-time optimization problem, providing a necessary and sufficient global optimality condition. Then, based on such condition we develop a continuous-time nonsmooth algorithm that is able to track the time-varying global optimal solution in finite-time. The proposed algorithm requires 2-hop neighborhood information that can be estimated by resorting to a state-of-the art finite-time k-hop distributed observer which can be implemented using only 1-hop information. Numerical results are provided to corroborate the theoretical findings.

Keywords: Distributed control, Optimal control, Numerical algorithms
Abstract: This paper extends the recently introduced ALADIN algorithm to non-convex continuous-time optimal control problems with nonlinear dynamics and linear coupling constraints. The algorithm alternates between solving a convexified local problem in a distributed manner and a linearized quadratic problem on a centralized entity while using the solution of both for an update step. This paper presents an analysis of the local convergence of the algorithm and shows a quadratic convergence rate. Furthermore, a globalization strategy is presented that ensures global convergence. The paper closes with a numerical evaluation of the algorithm.

Keywords: Distributed control
Abstract: This paper investigates the distributed average tracking problem for a group of double-integrator agents. In some practical applications, velocity measurements may be unavailable due to technology and space limitations, and it is also usually less accurate and more expensive to implement. To this end, a distributed average tracking algorithm without using velocity measurements and correct initialization is established. It is worth noting that no global information is needed for parameter design. Then, in order to remove the requirement on continuous interaction, and reduce the communication cost and improve the energy efficiency, an event-triggered distributed average tracking algorithm is designed by incorporating an event-triggered communication strategy without using velocity measurements. To be exact, the idea of a dynamic event-triggered strategy is used to construct a triggering condition for each agent to guarantee the exclusion of Zeno behavior. Finally, simulations are provided to illustrate the obtained results.

Keywords: Distributed control, Optimization algorithms, Agents-based systems
Abstract: In this work, we address the distributed optimization problem with event-triggered communication by the notion of input feedforward passivity (IFP). First, we analyze the distributed continuous-time algorithm over uniformly jointly strongly connected balanced digraphs in an IFP-based framework. Then, we propose a distributed event-triggered communication mechanism for this algorithm. Next, we discretize the continuous-time algorithm by the forward Euler method {with a constant stepsize irrelevant to network size}, and show that the discretization can be seen as a stepsize-dependent passivity degradation of the input feedforward passivity. Thus, the discretized system preserves the IFP property and enables the same event-triggered communication mechanism but without Zeno behavior due to the discrete-time nature. Finally, a numerical example is presented to illustrate our results.

Keywords: Distributed control, Networked control systems, Optimization
Abstract: This paper presents a novel distributed nonlinear protocol for minimizing the sum of convex objective functions in a fixed time under time-varying communication topology. In a distributed setting, each node in the network has access only to its private objective function, while exchange of local information, such as, state and gradient values, is permitted between the immediate neighbors. Earlier work in literature considers distributed optimization protocols that achieve convergence of the estimation error in a finite time for static communication topology, or under specific set of initial conditions. This study investigates first such protocol for achieving distributed optimization in a fixed time that is independent of the initial conditions, for time-varying communication topology. Numerical examples corroborate our theoretical analysis.

Keywords: Distributed parameter systems
Abstract: The use of mobile actuators for the control of spatially distributed systems governed by PDEs results in both implementational and computational challenges. First it requires the backward-in-time solution to the actuator guidance and the backward-in-time solution to the control operator Riccati equation. A way to address this computational challenge is to consider a continuous-discrete alternative whereby the mobile actuator is repositioned at discrete instances and resides in a specific spatial location for a certain time interval. In order to find optimal paths for a given time interval, a set of feasible locations is derived using the reachability set. These reachability sets are further constrained to take into account the time it takes to travel to any spatial position with a prescribed maximum velocity. The proposed hybrid continuous-discrete control and actuator guidance is demonstrated for a 2D diffusion PDE that uses no constraints and angular constraints on the actuator motion.

Keywords: Distributed parameter systems, Observers for Linear systems, Delay systems
Abstract: In this work, we study the observer design prob- lem for estimating thermoacoustic instabilities in a Rijke tube, using an in-domain point pressure measurement. Writing the system model in Riemann coordinates and, after a “folding transformation”, it takes the form of 4 × 4 linear hyperbolic partial differential equations (PDEs) coupled at the boundaries with a linear ordinary differential equation (ODE). This results in a PDE-ODE observer design problem, whose output is a combination of two infinite-dimensional states measured inside the domain. As a first step in our observer design, a “folding” transformation is applied around the measurement point, resulting in a 6 × 6 PDE-ODE system with measurements at one boundary. Then, the observer is designed as a copy of these equations plus an output injection term, which is given by a linear operator in the right-hand side of the ODE part. This operator is then chosen so that convergence of estimates is guaranteed by using stability properties of differential- delay systems. The design extends a previous result, based on backstepping, that required two measurements (both pressure and velocity). Simulation results are presented to illustrate the effectiveness of the proposed observer design.

Keywords: Distributed parameter systems, Observers for Linear systems, LMIs
Abstract: Finite-dimensional observer-based controller design for PDEs is a challenging problem. Recently, such controllers were introduced for the 1D heat equation, under assumption that at least one of the observation or control operators is bounded. This paper suggests a constructive method for such controllers in the case of where both the observation and control operators are unbounded. We consider boundary control of the 1D linear Kuramoto-Sivashinsky equation with in-domain point measurement. We employ a modal decomposition approach via dynamic extension, where we use the eigenfunctions of a Sturm-Liouville operator. The controller dimension is defined by the number of unstable modes, whereas the observer's dimension N may be larger than this number. We suggest a direct Lyapunov approach to the full-order closed-loop system and provide LMIs for finding N and the resulting exponential decay rate. We prove that the LMIs are always feasible, provided N is large enough. A numerical example demonstrates the efficiency of the method and shows that the resulting LMIs are non-conservative.

Keywords: Observers for nonlinear systems, Distributed parameter systems, Fluid flow systems
Abstract: The paper proposes a new homogeneous observer for finite-dimensional projections of quadratic homogeneous hyperbolic PDEs. The design relies upon new sufficient conditions for fixed-time convergence of observer's gain, described as a solution of a non-linear homogeneous matrix differential equations, towards an ellipsoid in the space of symmetric non-negative matrices. Convergence of the observer is analyzed, and a numerical convergence test is proposed: numerical experiments confirm the test on ODEs obtained by finite-difference discretization of Burgers-Hopf equation.

Keywords: Adaptive control, Distributed parameter systems, Nonlinear output feedback
Abstract: In an ultra-deep mining cable elevator, the guideway consists of several tensioned cables from the surface to thousands of meters underground. The interaction dynamics between the cage and the flexible guideway is approximate as a spring-damping system, and the cage is subject to external disturbances. Lateral vibration suppression of the mining cable elevator is addressed in this paper, where an adaptive output-feedback boundary controller is designed for coupled hyperbolic PDEs with spatially-varying coefficients and on a time-varying domain, of which the uncontrolled boundary is coupled by an ODE subject to uncertain disturbances. The asymptotic convergence to zero of the ODE state and the boundedness of the PDE states are proved via Lyapunov analysis. The performance of the proposed controller on lateral vibration suppression of a mining cable elevator is verified in the numerical simulation.

Keywords: Identification, Distributed parameter systems, Numerical algorithms
Abstract: This paper focuses on failure rate identification of a multi-state reparable system. The mathematical model is governed by coupled transport and integro-differential equations, which describe the probabilities of the system in good and failure modes. The objective of this work is to identify the failure rates based on the sampled-data of the probability of the system in good mode. Rigorous analysis is presented and numerical tests are conducted to demonstrate the design.

Keywords: Distributed parameter systems, Delay systems, LMIs
Abstract: In this paper, we present improved results on observer design for 1D heat equation. We first introduce an observer under delayed spatially point measurements that leads to an estimation error with time-delay. Inspired by recent developments in the area of delayed ODEs, we suggest augmented Lyapunov functionals based on the Legendre polynomials. Then, sufficient exponential stability conditions are derived in the form of linear matrix inequalities (LMIs) that are parameterized by the degree of the polynomials. Finally, a numerical example illustrates the efficiency of the results that allow to enlarge the value of delay preserving the stability by more than 20%.

Keywords: Distributed parameter systems
Abstract: This paper is about the finite-time steady-state to steady-state transfer of systems governed by boundary controlled 1D heat and beam equations. We address this problem using semi-discretization and flatness. We derive an n^{rm th}-order semi-discretized system of linear ODEs in time for the PDE system (which is either a heat equation or a beam equation) by approximating the spatial derivatives in the PDE system using Taylor's theorem. We show, under some regularity assumptions on the boundary input f and the initial state, that the state trajectory of the ODE systems converge to the state trajectory of the PDE system that they approximate as the number of discretization steps n goes to infinity. Given a T>0 and an initial steady-state u_0 at time t=0 and a final steady-state u_T at time t=T for the PDE system, we construct an input f_n for the n^{rm th}-order semi-discrete ODE system to transfer its state from discretized u_0 to discretized u_T in time T. This f_n is constructed using the flatness approach. We show that the sequence (f_n)_{n=1}^infty converges to a limiting function f as ntoinfty and f is the input that transfers the PDE system from u_0 to u_T. We illustrate our results using numerical simulations.

Keywords: Discrete event systems, Formal Verification/Synthesis, Automata
Abstract: In this paper, we investigate the problem of planning an optimal infinite path for a single robot to achieve a linear temporal logic (LTL) task with security guarantee. We assume that the external behavior of the robot, specified by an output function, can be accessed by a passive intruder (eavesdropper). The security constraint requires that the intruder should never infer that the robot was started from a secret location. We provide a sound and complete algorithmic procedure to solve this problem. Our approach is based on the construction of the twin weighted transition systems (twin-WTS) that tracks a pair of paths having the same observation. We show that the security-aware path planning problem can be effectively solved based on graph search techniques in the product of the twin-WTS and the Buchi automaton representing the LTL formula. The complexity of the proposed planning algorithm is polynomial in the size of the system model. Finally, we illustrate our algorithm by a simple robot planning example.

Keywords: Petri nets, Discrete event systems
Abstract: In this paper, we propose a semi-structural approach to verify some behavioural properties of bounded Petri nets, including home state existence, reversibility, liveness, and deadlock-freeness. An abstracted representation of the state space of Petri nets, called minimax basis reachability graph (minimax-BRG), is employed. We show how the verification of the above-mentioned properties for a bounded Petri net can be carried out testing equivalent properties of its corresponding minimax-BRG. Being the minimax-BRGs an abstracted representation of the reachability graph, the exhaustive enumeration of the state space can be avoided and we show, via numerical simulations, that this approach achieves significant practical efficiency.

Keywords: Discrete event systems, Automata
Abstract: Initial-state estimation consists in determining the initial state of the system based on the observation from the system and the system structure. It is the basis for many problems in security applications, such as opacity, detectability and supervisory control. However, when it comes to cyber-physical systems (CPS) communication delays and losses are inevitable. In this paper, we study the initial-state estimation problem in a CPS that is modeled with a multi-channel networked discrete event system (NDES). In practice, the system is usually distributed over several locations, and the communication between the system and an agent (e.g., intruder, observer, supervisor) is carried out via a shared network, in which communication delays and losses may happen. In multi-channel NDESs, even when the first-in first-out rule is satisfied in each channel, the order of events received by the agent may still be shuffled due to random communication delays in each channel. To address these new challenges, we formalize the initial-state estimation problem in multi-channel NDESs and a networked initial-state estimator is proposed to generate the exact initial-state estimate.

Keywords: Petri nets, Discrete event systems, Automata
Abstract: This paper studies the marking diagnosis problem in labeled Petri nets, i.e., to determine whether a plant has reached a given set of faulty markings or not in the past, from the observation history. We observe that the conventional basis reachability graphs cannot be used for marking diagnosis due to the existence of partially faulty basis markings. To overcome such a problem, we propose a notion called the diagnostic basis partition such that the corresponding basis reachability graphs does not contain any partially-faulty basis markings. By properly selecting a set of explicit transitions, a diagnostic agent is synthesized to perform the online diagnosis.

Keywords: Petri nets, Discrete event systems
Abstract: In this paper we study the optimal reconfiguration problem in Petri nets, i.e., to determine a firing sequence that drives a plant net from a source marking to a set of target markings with the minimal cost. We first propose a primitive breadth-first searching (BFS) algorithm that searches the basis marking space using minimal explanations and ILPs. Then we propose an improved BFS algorithm using a particular type of basis partitions that circumvents the need of solving ILPs. An optimal control sequence can be obtained using the cost tree constructed by the improved BFS algorithm.

Keywords: Optimal control, Networked control systems, Autonomous vehicles
Abstract: This paper studies the optimal stabilization control of the connected vehicle systems (CVSs). The CVS is expected to maintain a desired formation: each vehicle runs with a desired speed, and the distances between the vehicle and its neighbors are kept at desired values. The CVS dynamic is described by the discrete time difference equations. Each vehicle is able to measure its own speed, its nearest predecessor's speed and the distance between the vehicle and its nearest predecessor. Applying vehicle-to-vehicle (V2V) communication, the vehicle transmits its measured data to its nearest follower. Due to the uncertainties of the communication, it is stochastic that the data is effectively received. Under the above-mentioned setup, an optimal stabilization control framework is proposed for the CVS under the local stochastic communication. Based on system stability analysis and the optimization theory, the optimal stabilization control scheme is effectively designed. Finally, the simulation illustrates that the CVS is well maintained a desired formation under the proposed control scheme.

Keywords: Cooperative control, Optimization algorithms, Resilient Control Systems
Abstract: This paper is concerned with the distributed optimization problem where interagent communication is subject to DoS attacks. An event-based communication strategy is adopted to determine the signal transmission time, and then a resilient control algorithm is put forward to achieve consensus and meanwhile minimize the global objective function. By means of a positive invariant set and a quadratic Lyapunov functional, the convergence of the proposed algorithm is guaranteed. The effectiveness of the theoretical result is illustrated by a simulation example.

Keywords: Discrete event systems, Supervisory control, Automata
Abstract: This paper investigates attack mitigation problem in supervisory control of discrete event systems. We consider the scenario where the system is subject to actuator enablement attack. We explicitly distinguish between controllable events and defendable events; the former are events that can be disabled by the normal supervisor but may be subject to attack, while the latter are events that can be defensed (disabled definitely) by the mitigation module but possibly with higher costs. The objective is to design an attack mitigation strategy to prevent serious damage from attack. We formulate the attack mitigation problem as a tolerant control problem under partial observation. Particularly, in addition to guarantee safety, we aim to maximize the desirable behavior (normal specification) while minimize the tolerable behavior (safe but not desirable). We provide an effective online algorithm for solving this problem, which yields a novel attack mitigation strategy that generalizes the existing one in the literature. Specifically, we show that the proposed strategy may still prevent damage even when the safe-controllability condition, which is required by the existing strategy, does not hold.

Keywords: Stability of nonlinear systems, Algebraic/geometric methods
Abstract: Positive stabilization of a positive nonlinear system means feedback stabilization that preserves positivity of the system. It is shown that a positive nonlinear system on a time scale with bounded graininess function is positively stabilizable if its linearization is positively stabilizable with a feedback that preserves positivity of the nonlinear system. It is also proved that linearization preserves positivity of control systems. Positive stabilization of a linear positive system is a much easier task than positive stabilization of a nonlinear system, so the result presented in the paper may be used to positively stabilize nonlinear systems.

Keywords: Stability of nonlinear systems, Lyapunov methods
Abstract: In this paper, the stability problem of a class of planar positive nonlinear systems is investigated. Based on homogeneous nonlinear system theory and positive system theory, a necessary and sufficient condition for stability is established. To prove the necessity, a new method called special solution method is provided, and this method can be efficiently used to analyze instability. Three examples are provided to demonstrate the efficiency of the obtained results.

Keywords: Large-scale systems, Optimization, Linear systems
Abstract: In this work, we formulate two controllability maximization problems for large-scale networked dynamical systems such as brain networks: The first problem is a sparsity constraint optimization problem with a box constraint. The second problem is a modified problem of the first problem, in which the state transition matrix is Metzler. In other words, the second problem is a realization problem for a positive system. We develop a projected gradient method for solving the problems, and prove global convergence to a stationary point with locally linear convergence rate. The projections onto the constraints of the first and second problems are given explicitly. Numerical experiments using the proposed method provide some results that are difficult to deduce theoretically. In particular, the controllability characteristic is observed to change with increase in the parameter specifying sparsity, and the change rate appears to be dependent on the network structure.

Keywords: Compartmental and Positive systems, Linear systems
Abstract: This paper studies the variation diminishing property of linear time-invariant Hankel k-positive systems, i.e., systems whose Hankel operator maps inputs with k-1 sign changes to outputs with at most the same variation. Our main result is that these systems have a dominant approximation in the form of a parallel interconnection of k positive lags, that is, first order positive systems. This is shown by expressing the k-positivity of a LTI system as the external positivity (that is, 1-positivity) of k compound LTI systems. Our characterizations are generalizations of the well known properties of positive systems (k=1) and Hankel totally positive systems (k=infty).

Keywords: Uncertain systems, Estimation, Algebraic/geometric methods
Abstract: The vector field of a mixed-monotone system is decomposable via a decomposition function into increasing (cooperative) and decreasing (competitive) components, and this decomposition allows for, e.g., efficient computation of reachable sets and forward invariant sets. A main challenge in this approach, however, is identifying an appropriate decomposition function. In this letter, we show that any continuous-time dynamical system with a Lipschitz continuous vector field is mixed-monotone, and we provide a construction for the decomposition function that yields the tightest approximation of reachable sets when used with the standard tools for mixed-monotone systems. Our construction is similar to that recently proposed by Yang and Ozay for computing decomposition functions of discrete-time systems where we make appropriate modifications for the continuous-time setting and also extend to the case with unknown disturbance inputs. As in Yang’s and Ozay’s work, our decomposition function construction requires solving an optimization problem for each point in the state-space; however, we demonstrate through example how tight decomposition functions can sometimes be calculated in closed form. As a second contribution, we show how under-approximations of reachable sets can be efficiently computed via the mixed-monotonicity property by considering the backward-time dynamics.

Keywords: Stability of hybrid systems, Switched systems, Constrained control
Abstract: Projected dynamical systems (PDS), obtained by projecting a vector field on the tangent cone of a given constraint set, provide a convenient formalism to model constrained dynamical systems. When dealing with vector fields, which satisfy certain monotonicity properties, but not necessarily with respect to usual Euclidean norm, the resulting PDS does not necessarily inherit this monotonicity, as we will show. However, we demonstrate that if the projection is carried out with respect to a different norm, then the resulting “oblique PDS” preserves relevant monotonicity properties. This feature is specially desirable as it allows to guarantee important (incremental) stability notions and global asymptotic stability of periodic solutions (under periodic excitation) without having to carry out a difficult analysis on a PDS, which is a constrained discontinuous dynamical system. Instead, guaranteeing the mentioned properties for the original unconstrained dynamics, which is much easier, combined with choosing a “smart” projection leads directly to the desired properties for the PDS as well. This result is demonstrated by an application in the context of observer re-design guaranteeing that the state estimate lies in the same state set as the observed state trajectory.

Keywords: Constrained control, Linear systems, Predictive control for linear systems
Abstract: This paper deals with the analysis of the trajectories of autonomous dynamical systems with respect to static constraints. Two notions of constraints satisfaction and set-invariance are introduced in order to relax the classical definitions and offer a new perspective with potentially increased flexibility in the topology of the candidate sets. The relaxation comes from the possibility to violate the constraints for intervals of finite length along the evolution of the trajectory. In this line of developments, two alternative definitions emerge: a weak one which allows the validation of each constraint taken independently with an upper bound on the violation interval and the other one which imposes the length of the interval with a guarantee of constraint satisfaction. The main interest of those concepts is to handle simpler sets as positively invariant candidates with clear advantages in constrained control design.

Keywords: Stability of nonlinear systems, Numerical algorithms, Uncertain systems
Abstract: This work presents new tools for studying reachability and set invariance for continuous-time mixed-monotone dynamical systems subject to a disturbance input. The vector field of a mixed-monotone system is decomposable via a decomposition function into increasing and decreasing components, and this decomposition enables embedding the original dynamics in a higher-dimensional embedding system. While the original system is subject to an unknown disturbance input, the embedding system has no disturbances and its trajectories provide bounds for finite-time reachable sets of the original dynamics. Our main contribution is to show how one can efficiently identify robustly forward invariant and attractive sets for mixed-monotone systems by studying certain equilibria of this embedding system. We show also how this approach, when applied to the backward-time dynamics, establishes different robustly forward invariant sets for the original dynamics. Lastly, we present an independent result for computing decomposition functions for systems with polynomial dynamics. These tools and results are demonstrated through several examples and a case study.

Keywords: Distributed control, Linear systems, Output regulation
Abstract: In this paper, the problem of modal consensus of a network of agents is considered. We introduce the notion of "disagreement interaction" and we propose a distributed control design strategy that minimizes such potentially detrimental interaction between the agents. The above concepts are then specialized to a multi-agent system consisting of single integrators. The proposed solution does not introduce additional dynamics to the system anywhere in the network. It is shown that the minimization of the disagreement interaction results in the feature that the agents exchange the information strictly necessary to induce an endogenous internal model, while limiting any other interaction, which may even induce instability of the system.

Keywords: Output regulation, Linear systems, LMIs
Abstract: This paper addresses the problem of dynamic output feedback controller design for linear two time-scales dynamics. Unlike most of the works in the literature on singularly perturbed systems, we also consider the case where the state matrix of the fast dynamics is singular (nonstandard systems) and unstable. Our approach relies on decoupling the slow and fast dynamics of the closed-loop system and applying algebraic manipulations based on Finsler's Lemma to obtain epsilon-dependent and epsilon-independent controllers. The design conditions are computationally oriented since they are expressed in term of Linear Matrix Inequalities (LMIs). On top of this, a quadratic cost is guaranteed to be upper-bounded for all positive values of the singular parameter. The proposed conditions circumvent some drawbacks of the existing works on this topic by providing a dynamic controller that does not depend on the singular parameter. A numerical example illustrates the effectiveness of the proposed approach.

Keywords: Output regulation, Nonlinear output feedback
Abstract: The increase in system complexity paired with a growing availability of operational data has motivated a change in the traditional control design paradigm. Instead of modeling the system by first principles and then proceeding with a (model-based) control design, the data-driven control paradigm proposes to directly characterize the controller from data. By exploiting a fundamental result of Willems and collaborators, this approach has been successfully applied to linear systems, yielding data-based formulas for many classical linear controllers. In the present paper, the data-driven approach is extended to a class of nonlinear systems, namely second-order discrete Volterra systems. Two main contributions are made for this class of systems. At first, we show that - under a necessary and sufficient condition on the input data excitation - a data-based system representation can be derived from input-output data and used to replace an explicit system model. That is, the fundamental result of Willems et al. is extended to this class of systems. Subsequently a data-driven internal model control formula for output-tracking is derived. The approach is illustrated via two simulation examples.

Keywords: Output regulation, Stability of nonlinear systems
Abstract: This paper deals with a tracking problem for nonlinear systems. We present sufficient conditions for the state-feedback output tracking problem, in case of arbitrarily large constant references and arbitrarily large domain of attraction. We present an extension of forwarding-based control techniques applied in an incremental framework.

Keywords: Output regulation, Time-varying systems, Power systems
Abstract: In this letter, we propose a novel control scheme for regulating the voltage in Direct Current (DC) power networks. More precisely, the proposed control scheme is based on the output regulation methodology and, differently from the results in the literature, where the loads are assumed to be constant, we consider time-varying loads whose dynamics are described by a class of nonlinear differential equations. We prove that the proposed control scheme achieves voltage regulation ensuring the stability of the overall network.

Keywords: Cooperative control, Nonlinear output feedback, Output regulation
Abstract: In this paper, we study the event-triggered cooperative global robust practical output regulation problem for nonlinear multi-agent systems in output feedback with any relative degree. By establishing some new technical lemmas, and integrating the distributed internal model approach and the distributed hybrid observer approach, we recursively construct a distributed output-based event-triggered control law and a distributed output-based Zeno-free event-triggered mechanism to solve our problem.

Keywords: Delay systems, Stability of linear systems, Output regulation
Abstract: The note studies the stabilization problem for a SISO continuous-time plant, where the feedback loop contains a fixed infinite-dimensional repetitive element and a "primary controller" to be designed. A novel architecture of the primary controller is proposed, which reduces the stabilization problem to that for a finite-dimensional system. The architecture has a flavor of dead-time compensation, also in the structure of resulting closed-loop systems. In the minimum-phase case, an implementation scheme insensitive to the value of the delay in the repetitive block is proposed.

Keywords: Predictive control for nonlinear systems, Output regulation, Stability of nonlinear systems
Abstract: In this paper, we show that a simple model predictive control (MPC) scheme can solve the constrained nonlinear output regulation problem without explicitly solving the classical regulator (Francis-Byrnes-Isidori) equations. We first study the general problem of stabilizing a set with MPC using a positive semidefinite (input/output) cost function under suitable stabilizability and detectability assumptions, similar to Grimm et al. (2005). We show that in the output regulation setting, these conditions hold, if the nonlinear constrained regulation problem is (strictly) feasible, the plant is incrementally stabilizable, incrementally input-output to state stable (i-IOSS) and the control input can be uniquely reconstructed from the plant/reference output. Given these structural assumptions, by simply penalizing the predicted output error in the MPC stage cost, the closed loop implicitly stabilizes a state trajectory that solves the regulator equations, if a sufficiently large prediction horizon is used.

Keywords: Robotics, Biologically-inspired methods, Stability of nonlinear systems
Abstract: Snake robots are motivated by the slender and flexible body of biological snakes, which allows them to move in virtually any environment on land and in water. Since the snake robot is essentially a manipulator arm that can move by itself, it has a number of interesting applications including firefighting and search-and-rescue operations. In water, the robot is a highly flexible and dexterous manipulator arm that can swim by itself like a sea snake. This highly flexible snake-like mechanism has excellent accessibility properties, and not only can the snake robot access narrow openings and confined areas, it can also carry out highly complex manipulation tasks at this location since manipulation is an inherent capability of the system.

This talk presents research results on modelling, analysis and control of snake robots, including both theoretical and experimental results. Ongoing efforts are described for bringing the results from university research towards industrial use.

Keywords: Network analysis and control, Estimation, Compartmental and Positive systems
Abstract: Motivated by the ongoing pandemic COVID-19, we propose a closed-loop framework that combines inference from testing data, learning the parameters of the dynamics and optimal resource allocation for controlling the spread of the susceptible-infected-recovered (SIR) epidemic on networks. Our framework incorporates several key factors present in testing data, such as high risk individuals are more likely to undergo testing and infected individuals potentially act as asymptomatic carriers of the disease. We then present two tractable optimization problems to evaluate the trade-off between controlling the growth-rate of the epidemic and the cost of non-pharmaceutical interventions (NPIs). Our results provide compelling insights for policy-makers, including the significance of early testing and the emergence of a second wave of infections if NPIs are prematurely withdrawn.

Keywords: Distributed control, Control of networks, Biological systems
Abstract: Among the many mathematical models in epidemiology, the deterministic SIS Network model is a fundamental one which has been studied extensively by various scientific communities. On strongly connected networks, it is well known that there exists an endemic equilibrium (the disease persists in all nodes of the network) if and only if the reproduction number of the network system is greater than 1. In fact, the endemic equilibrium is unique and is asymptotically stable for all feasible nonzero initial conditions. This talk investigates the use of control in order to drive the network system to the healthy equilibrium (where every node is disease free). We consider a broad class of distributed feedback controllers, with the recovery rate of each node being the control input. We illustrate the significant challenges involved in feedback control when the uncontrolled network system has a reproduction number greater than 1, but also highlight some benefits. We then discuss the results and their implications, laying groundwork for the further development of feedback control approaches to tackling epidemic spread over networks.

Keywords: Control of networks, Biological systems, Stochastic optimal control
Abstract: Mitigation of the novel coronavirus has required control programs at the societal scale (e.g. shelter-in-place orders, closure of businesses and facilities, quarantine policies, travel restrictions). The economic and social impacts of these controls are enormous, hence government authorities and the general public are naturally anxious to quickly ease the controls. Yet, easing the controls seems to carry considerable risk, as doing so would again allow for exponential growth in case counts -- in system-theoretic terms, cause the null equilibrium of the system to revert to instability. The intrinsic challenge associated with easing controls is further compounded by the significant inertia inherent to enacting and modifying these societal-scale policies. The purpose of this talk is to explore how network-theoretic modeling and controls-engineering concepts can be brought to bear to design the removal or easing of infectious-disease controls. With this goal in mind, I will: 1) brainstorm the factors which impact infectious disease evolution after controls are eased, 2) describe network models that may be useful for studying the easing of controls, and 3) scope control-design problems that may arise in this space.

Keywords: Healthcare and medical systems, Control of networks, Network analysis and control
Abstract: The ongoing COVID-19 pandemic is caused by a novel coronavirus identified in December 2019 and currently sweeping the world. Since the first case reported, the virus has spread rapidly all over the world. The pandemic clearly shows that in metapopulations, the most serious source of infection and disease spreading is due to infected individuals traveling between populations. During this period, each country or state adopted different travel restriction and lockdown policies at different points in time. It is important to fully understand and quantify the effects of those polices so that we can know what strategies are best to face the expected next wave or future outbreaks. There are few mathematical models which attempt to capture the dynamics of epidemic spreading over metapopulations with social distancing, travel restriction, and lockdown policies, let alone their applications have been limited to theoretical and numerical analyses. Past experience shows that coordinating mitigation efforts among countries and states is a difficult task, and sometimes even impossible, due to different governmental and social norms and practices. Meanwhile, there are significant differences in COVID-19 detecting capacities, which causes varying delays in reporting the confirmed cases. Detection and control of the virus spreading thus require robust and distributed strategies. Almost all the existing control and decision approaches do not explicitly capture these uncertainties and require centralized implementations.

The goal of this panel is to initiate discussions on how we can establish a resilient framework which can detect, respond and control the next wave or future pandemic outbreaks in a real-time and distributed manner.

Several natural questions, important also for policy making, arise: - How do we model and quantify the effects of social distancing, travel restriction, and lockdown policies? - How much more effective would mandated shelter-in-place be in containing the spread, compared with other practices? - Is it worth the social cost? What is the effect of 10% of the population ignoring these protocols? - How do we effectively track the confirmed and suspected cases? - How do we coordinate mitigation efforts among different regions? - What is the optimal length of quarantine? - How do we efficiently use the collected data?

Keywords: Systems biology, Biomolecular systems, Stochastic systems
Abstract: Metabolic networks are known to deal with the chemical reactions responsible to fuel cellular activities with energy and carbon source and, as a matter of fact, to set the growth rate of the cell. To this end, feedback and regulatory networks play a crucial role to handle adaptation to external perturbations and internal noise. In this work, a cellular resource is assumed to be activated at the end of a metabolic pathway, by means of a cascade of transformations. Such a cascade is triggered by the catalytic action of enzymes that promote the transformations. The final product is responsible for the cellular growth rate modulation. This mechanism acts in feedback at the enzymatic level, since the upstream enzyme (as well as all species) is subject to clearance, with the clearance rate proportional to growth. The upstream enzymatic production is modeled by the occurrence of noisy bursts: a Stochastic Hybrid System is exploited to model the network and to investigate how such noise propagates on growth fluctuations. A major biological finding is that the delay introduced by the cascade length helps in reducing the impact of enzymatic noise on to growth fluctuations. Further, if feedback is removed from the scheme, growth rate fluctuations increase, according to the same stationary values. Analytical results are supported by Monte Carlo simulations

Keywords: Systems biology, Filtering, Biomolecular systems
Abstract: We consider the problem of estimating the dynamic latent states of an intracellular multiscale stochastic reaction network from time-course measurements of fluorescent reporters. We first prove that accurate solutions to the filtering problem can be constructed by solving the filtering problem for a reduced model that represents the dynamics as a hybrid process. The model reduction is based on exploiting the time-scale separations in the original network, and it can greatly reduce the computational effort required to simulate the dynamics. This enables us to develop efficient particle filters to solve the filtering problem for the original model by applying particle filters to the reduced model. We illustrate the accuracy and the computational efficiency of our approach using a numerical example.

Keywords: Estimation, Biomedical
Abstract: A novel estimation algorithm for the times and weights of a finite number of impulses constituting the input signal of a known continuous linear time-invariant system from the output signal of the latter is proposed. The intended application area is the estimation of pulsatile input in biomedical systems. The output signal is assumed to belong to L2 and be represented in Laguerre domain. A generalization of the Laguerre domain to distributions is utilized to incorporate Dirac delta-functions into the mathematical framework. The estimation algorithm utilizes the Laguerre parameter p to regularize an otherwise ill-conditioned problem. The viability of the method is demonstrated on simulated and experimental data exhibiting a double-peak decay in the concentration of an anti-Parkinsonian drug after a single dose administration.

Keywords: Biological systems, Discrete event systems
Abstract: Discrete-time models are the traditional approach for capturing population dynamics of insects living in the temperate regions of the world. These models are characterized by an update function that connects the population densities from one year to the next. We revisit classical discrete-time models used for modeling interactions between two insect species (a host and a parasitoid), and provide novel result on the stability of the population dynamics. In particular, for a class of models we show that the fixed point is stable, if and only if, the host equilibrium density is an increasing function of the host's reproduction rate. We also introduce a hybrid approach for obtaining the update functions by solving ordinary differential equations that mechanistically capture the ecological interactions between the host and the parasitoid. This hybrid approach is used to study the suppression of host density by a parasitoid. Our analysis shows that when the parasitoid attacks the host at a constant rate, then the host density cannot be suppressed beyond a certain point without making the population dynamics unstable. In contrast, when the parasitoid's attack rate increases with increasing host density, then the host population density can be suppressed to arbitrarily low levels. These results have important implications for biological control where a natural enemy, such as a parasitoid wasp, is introduced to eliminate a pest that is the host species for the parasitoid.

Keywords: Biological systems, Biomedical
Abstract: Adoptive transfer of chimeric antigen receptor (CAR)-engineered T cells has demonstrated durable clinical efficacy in patients with hematologic malignancies and is currently being investigated as a therapeutic approach to solid tumors. One of the major challenges underlying its success arises from the inability to effectively target the diversity, expression, and cell surface distribution of tumor-associated antigens (TAA) characteristic of solid tumors. Antigen escape is likely—CAR T cells targeting a single antigen can drive the emergence of minor, co-existing clonal populations lacking antigen expression—thereby promoting tumor progression. This paper presents a cellular immunotherapy model that describes the dynamics of cancer growth and response to CAR T cell therapy and a receding horizon control formulation to synthesize switching treatment strategies that maximize tumor regression while satisfying safety constraints with respect to therapy induced toxicity. We illustrate the algorithm and show that temporal dosing schedules can control tumors with heterogeneous antigen expression. This model sets a framework by which to assess the effectiveness of adaptive CAR T cell treatment strategies, clinical trial design and patient stratification.

Keywords: Time-varying systems, LMIs, Stability of linear systems
Abstract: A method for determining whether a linear time-varying (LTV) system is exponentially stable has been proposed based on differential Lyapunov inequalities (DLIs). However, there are few established systematic methods to find solutions of DLIs. In this paper, we focus on a class of periodic LTV systems and propose a method to find solutions of DLIs by using linear matrix inequalities (LMIs). Moreover, we propose a method to design state observers, state feedback controllers and output feedback controllers for periodic LTV systems by utilizing the proposed DLI solutions search method. Some examples show the effectiveness of the proposed analysis and design method.

Keywords: Lyapunov methods, Stability of nonlinear systems, Discrete event systems
Abstract: In this article, we study the problem of asymptotic stabilization for nonlinear affine discrete-time control systems with periodic coefficients via state feedback. It is supposed that the origin of the free dynamic system is (non-asymptotically) stable. The method for constructing a damping control is extended from time-invariant systems to time varying periodic affine discrete-time systems. This method is based on the Krasovsky-La Salle invariance principle for periodic systems. Using this approach, we obtain sufficient conditions for uniform local and global asymptotic stabilization for those systems.

Keywords: Linear parameter-varying systems, Numerical algorithms, Optimization algorithms
Abstract: A continuation method is applied to compute the H_infty gain of a periodic linear system. The H_infty gain of a periodic linear system can be equivalently found by solving a Periodic Differential Riccati Equation (PDRE) for an increasing sequence of gain candidates until no solution exists. Solving the PDRE can be cumbersome. However, for a null gain candidate, the PDRE is a Periodic Differential Lyapunov Equation (PDLE) that can be solved efficiently. Similarly, for a small increase in the gain candidate, the solution can be approximated by solving another PDLE. We describe an application of the continuation method where the corrector uses a Boundary Value Problem solver. Therefore, using a continuation method can be promising for such a problem. The gain candidate is increased until no solution to the PDRE exists. Compared to Hamiltonian based approaches, our approach suffers less from ill-conditioned differential equations for systems where the periodicity is long compared to the dynamic of the system of interest.

Keywords: Subspace methods, Identification, Time-varying systems
Abstract: This letter proposes a new methodology for subspace identification of linear time-periodic (LTP) systems with periodic inputs. This method overcomes the issues related to the computation of frequency response of LTP systems by utilizing the frequency response of the time-lifted system with linear time-invariant structure instead. The response is estimated with an ensemble of input-output data with periodic inputs. This allows the frequency-domain subspace identification technique to be extended to LTP systems. The time-aliased periodic impulse response can then be estimated and the order-revealing decomposition of the block-Hankel matrix is formulated. The consistency of the proposed method is proved under mild noise assumptions. Numerical simulation shows that the proposed method performs better than multiple widely-used time-domain subspace identification methods when an ensemble of periodic data is available.

Keywords: Aerospace, Predictive control for linear systems
Abstract: In this paper, an MPC solution is devised for linear time-periodic optimal regulation problems requiring the minimization of a sum of vector norms. Such type of problems arise for instance in aerospace applications, in which it is desired to trade-off fuel consumption and state regulation performance, while limiting as much as possible the control activation time. Closed-loop stability is guaranteed by embedding in the design a terminal set and a terminal cost, both of which are periodically time-varying. Differently from quadratic MPC, the terminal cost is in the form of a weighted 2-norm. A systematic method to construct such a function is presented. The proposed design is demonstrated on a spacecraft rendezvous case study with periodic dynamics.

Keywords: Iterative learning control, Machine learning, Optimization algorithms
Abstract: Model-free reinforcement learning techniques directly search over the parameter space of controllers. Although this often amounts to solving a nonconvex optimization problem, for benchmark control problems simple local search methods exhibit competitive performance. To understand this phenomenon, we study the discrete-time Linear Quadratic Regulator (LQR) problem with unknown state-space parameters. In spite of the lack of convexity, we establish that the random search method with two-point gradient estimates and a fixed number of roll-outs achieves epsilon-accuracy in O(log (1/epsilon)) iterations. This significantly improves existing results on the model-free LQR problem which require O(1=epsilon) total roll-outs.

Keywords: Neural networks, Lyapunov methods, Control applications
Abstract: Crafting adversarial inputs for attacks on neural networks and robustification against such attacks have continued to be a topic of keen interest in the machine learning community. Yet, the vast majority of work in current literature is only empirical in nature. We present a novel viewpoint on adversarial attacks on recurrent neural networks (RNNs) through the lens of dynamical systems theory. In particular, we show how control theory-based analysis tools can be leveraged to compute these adversarial input disturbances, and obtain bounds on how they impact the neural network performance. The disturbances are computed dynamically at each time-step by taking advantage of the recurrent architecture of RNNs, thus making them more efficient compared to prior work, as well as amenable to `real-time' attacks. Finally, the theoretical results are supported by some illustrative examples.

Keywords: Neural networks, Optimization, Statistical learning
Abstract: In this paper, we consider gradient descent on a regularized loss function for training an overparametrized neural network. We model the algorithm as an ODE and show how overparameterization and regularization work together to provide the right tradeoff between training and generalization errors.

Keywords: Energy systems, Cyber-Physical Security, Control Systems Privacy
Abstract: In this paper, we consider the problem of optimally coordinating the response of a set of distributed energy resources (DERs) for serving the needs of a set of electrical loads while protecting the privacy of consumer usage data. The DERs are coordinated via a distributed approach that relies on an averaging step for guiding DERs towards the optimal operating point. Since naive exchanges of information during the averaging step might reveal sensitive information about personal energy consumption, we incorporate homomorphic encryption into the averaging step to enforce electricity usage privacy. To carry out such a procedure, power consumption data collected at electrical loads are first quantized and encrypted using the Paillier homomorphic cryptosystem. The averaging step is then executed using the homomorphically encrypted version of the so-called ratio consensus algorithm that operates exclusively on integer values. We further analytically show that the use of homomorphic encryption does not significantly affect the performance of the distributed scheme, and prove that the resulting homomorphically encrypted distributed algorithm achieves geometric convergence speed over directed communication graphs with packet losses. We showcase the proposed algorithm using the standard IEEE 14-bus test system.

Keywords: Optimization algorithms, Machine learning
Abstract: Difference-of-convex (DC) optimization problems are shown to be equivalent to the minimization of a Lipschitz-differentiable ``envelope''. A gradient method on this surrogate function yields a novel (sub)gradient-free proximal algorithm which is inherently parallelizable and can handle fully nonsmooth formulations. Newton-type methods such as L-BFGS are directly applicable with a classical linesearch. Our analysis reveals a deep kinship between the novel DC envelope and the forward-backward envelope, the former being a smooth and convexity-preserving nonlinear reparametrization of the latter.

Keywords: Flight control, Kalman filtering, Formal Verification/Synthesis
Abstract: This paper introduces a novel methodology based on the zonotopic Kalman filtering for stabilizing attitude dynamics and estimating flight envelopes of an unmanned helicopter via observer-based feedback control and reachability analysis, respectively. The helicopter dynamics is represented by a linear state-space model, based on which the feedback control law is designed. To acquire full state information, the zonotopic Kalman filter is applied to yield sets of state-variable estimates of the helicopter in terms of zonotopes. Not only are the resulting zonotopes used for the observer-based feedback control, but also for estimating the flight envelopes of the helicopter based on the reachability analysis. This approach is useful for enhancing pilot's awareness about dynamic responses of the helicopter, which may undergo unsafe flight conditions due to actuator faults triggered by undesirable perturbations such as icing conditions. The efficacy of the proposed methodology is demonstrated via an example, where we also expose the benefits of applying the zonotopic Kalman filter as compared with an ordinary stochastic Kalman filter.

Keywords: Flight control, Fault tolerant systems, Observers for Linear systems
Abstract: This article presents a design example of Fault-Tolerant Flight Controllers (FTFCs) and their performance assessment via Hardware-In-the-Loop (HIL) tests with a real airplane. An observer-based robust H_{infty} design approach is proposed where the states of the observers can be used as virtual sensors for Fault Detection and Isolation (FDI). Two observer-based robust H_{infty} FTFCs against actuator faults are designed based on whether the observer performance is optimized or not. Their control and observer performances are compared via HIL tests with JAXA's research airplane MuPAL-alpha.

Keywords: Machine learning, Flight control, Iterative learning control
Abstract: This paper presents a combination of reinforcement learning (RL) and deterministic controllers to learn a quadrotor control. Learning the quadrotor flight in a standard RL approach requires many iterations of trial and error, which may bring about risky exploration and battery consumption. In this paper, we integrate a classical controller such as PD (proportional and derivative) or LQR (linear quadratic regulator) with a RL policy using their linear combination. The proposed method is not only simple to use, but also fast in learning convergence. When the algorithm is evaluated for a quadrotor trajectory tracking by means of a velocity control for both simulation and experiment, it demonstrates the faster convergence rate and better control performance.

Keywords: Flight control, Variable-structure/sliding-mode control, Robust control
Abstract: This paper synthesizes a C1 smooth, continuous, output-tracking sliding mode controller for a full-scale helicopter operating in high-intensity turbulence. The closed-loop dynamics are required to satisfy ideal on-axis attitude and rate response characteristics. Additionally, robust command tracking and suppression of off-axis responses are required in the presence of matched and unmatched uncertainties. Lyapunov based theoretical proofs are utilized for the tracking problem via application of a continuous second-order sliding mode (SOSM) controller. A second order sliding mode observer is employed to estimate the higher derivatives of the sliding variable for the output feedback controller. Simulations in hover illustrate the continuity, smoothness, and robustness properties of the proposed controller as compared to a conventional sliding mode controller and a linear quadratic controller.

Keywords: Adaptive control, Robust adaptive control, Flight control
Abstract: Control of fixed-wing Unmanned Aerial Vehicles (UAVs) is typically organized according to two layers: the lowlevel control or autopilot, and the high-level control or guidance. The disadvantage of this modular design is that an intelligent guidance layer may become ineffective if the autopilot layer cannot deal with uncertainty. In fact, the required knowledge derived from linearization of equations of motion (trimming points) makes most autopilots sensitive to uncertainty. In this work, we study an autopilot framework where the knowledge of the UAV dynamics and of trimming points is not required. The proposed design, tested with complex UAV dynamics, can emulate the behavior of a carefully tuned off-the-shelf autopilot, without using its a priori knowledge.

Keywords: Distributed control, Networked control systems, Adaptive control
Abstract: The attitude consensus problem of multiple rigid body systems has been studied via the adaptive distributed observer approach. However, the current adaptive distributed observer needs to recover the full state of the leader system, which leads to a high dimension distributed control law. In this paper, we further solve the same problem by utilizing the recently developed output based adaptive distributed output observer. The new approach has the advantages that it only relies on the output instead of the state of the target system and the dimension of the resultant control law can be significantly lower than that of the existing adaptive distributed observer based control laws.

Keywords: Networked control systems, Communication networks, Control of networks
Abstract: Multi-agent consensus systems have been investigated in the continuous-time setting in regard to the control design, their scalability, and their robustness to interference. The discrete-time setting lacks the same depth of investigation. This paper investigates discrete-time multi-agent consensus systems. In particular, we propose a new controller design. The design uses a linear controller that is independent of the number of agents connected and imposes a single constraint on the communication structure. This is a step towards a scalable multi-agent consensus system that allows simple connection of additional agents without readjustments to the controller.

Keywords: Cooperative control
Abstract: In this paper, we formulate and investigate the leader-following almost output consensus problem for linear multi-agent systems with disturbance affected unstable zero dynamics. Conditions on the communication topology, agent dynamics and the way the disturbances affect the zero dynamics are established under which low-and-high gain based consensus protocols are designed. These protocols are shown to achieve leader-following almost output consensus, that is, output consensus of the system can be achieved to an arbitrary level of accuracy with the states remain bounded in the absence of the disturbances, and when the system is operating in output consensus within the desired accuracy, the L_2-gain from the disturbances to the difference between each follower agent's output with and without the disturbances from the same initial condition can be made arbitrarily small.

Keywords: Agents-based systems, Optimal control, Stability of nonlinear systems
Abstract: This paper addresses the optimal formation control problem of a multi-agent system. The foraging behavior of N agents is modeled as an infinite-horizon non-cooperative differential game under local information, and its Nash equilibrium is studied. The formations are achieved in an intrinsic way in the sense that they are only attributed to the inter-agent interaction and geometric properties of the network, where the desired formations are not designated beforehand. Through the design of individual costs and network topology, patterns of Platonic solids can be achieved as Nash equilibria while inter-agent collisions are avoided. Exponential convergence to the manifold of Platonic patterns is proved. Finally, numerical simulations are provided to demonstrate the effectiveness and feasibility of the proposed methods.

Keywords: Agents-based systems, Cooperative control, Distributed control
Abstract: This paper addresses a formation tracking problem for nonlinear multi-agent systems with time-varying actuator faults. In the directed leader-follower network, only a small subset of agents can receive the nonlinear leader’s information. The aforementioned setting improves the practical relevance of addressed problem and meanwhile, it poses technical challenges to the controller design and asymptotic convergence analysis. By introducing a distributed estimation and control framework, a novel distributed control law using a Nussbaum gain technique is developed to achieve robust fault-tolerant formation tracking for heterogeneous nonlinear multi-agent systems over a digraph with a spanning tree. Numerical simulation results are given to verify the effectiveness of the proposed method.

Keywords: Identification for control, Nonlinear systems identification, Learning
Abstract: In this paper, we establish an iterative data-driven approach to derive guaranteed bounds on nonlinearity measures of unknown nonlinear systems. In this context, nonlinearity measures quantify the strength of the nonlinearity of a dynamical system by the distance of its input-output behaviour to a set of linear models. First, we compute a guaranteed upper bound of these measures by given input-output samples based on a data-based non-parametric set-membership representation of the ground-truth system and local inferences of nonlinearity measures. Second, we propose an algorithm to improve this bound iteratively by further samples of the unknown input-output behaviour.

Keywords: Identification, Linear systems, Identification for control
Abstract: Willems et al.'s fundamental lemma asserts that all trajectories of a linear system can be obtained from a single given one, assuming that a persistency of excitation and a controllability condition hold. This result has profound implications for system identification and data-driven control, and has seen a revival over the last few years. The purpose of this paper is to extend Willems' lemma to the situation where multiple (possibly short) system trajectories are given instead of a single long one. To this end, we introduce a notion of collective persistency of excitation. We will show that all trajectories of a linear system can be obtained from a given finite number of trajectories, as long as these are collectively persistently exciting. We will demonstrate that this result enables the identification of linear systems from data sets with missing samples. Additionally, we show that the result is of practical significance in data-driven control of unstable systems.

Keywords: Identification, Linear systems, Identification for control
Abstract: The fundamental lemma due to Willems et al. ``A note on persistency of excitation,'' Syst. Control Lett., vol. 54, no. 4, pp. 325--329, 2005 plays an important role in system identification and data-driven control. One of the assumptions for the fundamental lemma is that the underlying linear time-invariant system is controllable. In this paper, the fundamental lemma is extended to address system identification for uncontrollable systems. Then, a data-driven algebraic test is derived to check whether the underlying system is controllable or not. An algorithm based on the singular value decomposition of a Hankel matrix constructed from the data is provided to implement the developed test. The algorithm has cubic computational cost. Examples are given to illustrate the theoretical results.

Keywords: Estimation, Filtering, Uncertain systems
Abstract: This paper presents a novel data-driven, direct filtering approach for unknown linear time-invariant systems affected by unknown-but-bounded measurement noise. The proposed technique combines independent multistep prediction models, identified resorting to the Set Membership framework, to refine a set that is guaranteed to contain the true system output. The filtered output is then computed as the central value in such a set. By doing so, the method achieves an accurate output filtering and provides tight and minimal error bounds with respect to the true system output. To attain these results, the online solution of linear programs is required. A modified filtering approach with lower online computational cost is also presented, obtained by moving the solution of the optimization problems to an offline preliminary phase, at the cost of larger accuracy bounds. The performance of the proposed approaches are evaluated and compared with those of standard model-based filtering techniques in a numerical example.

Keywords: Iterative learning control, Autonomous systems, Machine learning
Abstract: In this paper, we study online regulation of partially unknown (and possibly unstable) linear systems. In order to avoid the popular assumption of having access to an initial stabilizing controllers in learning algorithms, we propose the Data-Guided Regulator (DGR) synthesis that regulates the underlying states of an unknown linear model through generating informative data. We also introduce the notion of "regularizability" for a linear system that is of independent interest and provides a unique perspective on the geometry of data-guided regulation. Finally, we discuss an example involving online regulation of the (open-loop unstable) X-29 aircraft.

Keywords: Filtering, Machine learning, Variational methods
Abstract: In this paper, we present a novel approach to approximate the gain function of the feedback particle filter (FPF). The exact gain function is the solution of a Poisson equation involving a probability-weighted Laplacian. The numerical problem is to approximate the exact gain function using only finitely many particles sampled from the probability distribution.

Inspired by the recent success of the deep learning methods, we represent the gain function as a gradient of the output of a neural network. Thereupon considering a certain variational formulation of the Poisson equation, an optimization problem is posed for learning the weights of the neural network. A stochastic gradient algorithm is described for this purpose.

The proposed approach has two significant properties/advantages: (i) The stochastic optimization algorithm allows one to process, in parallel, only a batch of samples (particles) ensuring good scaling properties with the number of particles; (ii) The remarkable representation power of neural networks means that the algorithm is potentially applicable and useful to solve high-dimensional problems. We numerically establish these two properties and provide extensive comparison to the existing approaches.

Keywords: Filtering, Optimization, Algebraic/geometric methods
Abstract: A class of nonlinear matched filters is introduced suitable for detection problems using Chen--Fliess functional series. Such series can be viewed as a noncommutative analogue of Taylor series. They are written in terms of a weighted sum of iterated integrals indexed by words over a noncommuting set of symbols. The primary goal is to identify within this class the set of filters which maximizes the signal-to-noise ratio at a given time instant in order to provide a statistic for detecting a known signal.

Keywords: Filtering, Estimation, Stochastic systems
Abstract: We present a novel dual quaternion filter for recursive estimation of rigid body motions. Based on the sequential Monte Carlo scheme, particles are deployed on the manifold of unit dual quaternions. This allows non-parametric modeling of arbitrary distributions underlying on the SE(3) group. The proposal distribution for importance sampling is estimated particle-wise by a novel dual quaternion unscented Kalman filter (DQ-UKF). It is adapted to the manifold geometric structure and drives the prior particles towards high-likelihood regions on the manifold. The resultant unscented dual quaternion particle filter (U-DQPF) incorporates the most recently observed evidence, raising the particle efficiency considerably for nonlinear pose estimation tasks. Compared with ordinary particle filters and other parametric model-based dual quaternion filtering schemes, the proposed U-DQPF shows superior performance in nonlinear SE(3) estimation.

Keywords: Estimation, Filtering, Machine learning
Abstract: We consider incremental inference problems from aggregate data for collective dynamics. In particular, we address the problem of estimating the aggregate marginals of a Markov chain from noisy aggregate observations in an incremental (online) fashion. We propose a sliding window Sinkhorn belief propagation (SW-SBP) algorithm that utilizes a sliding window filter of the most recent noisy aggregate observations along with encoded information from discarded observations. Our algorithm is built upon the recently proposed multi-marginal optimal transport based SBP algorithm that leverages standard belief propagation and Sinkhorn algorithm to solve inference problems from aggregate data. We demonstrate the performance of our algorithm on applications such as inferring population flow from aggregate observations.

Keywords: Estimation, Algebraic/geometric methods, Filtering
Abstract: This paper proposes a symbolic-numeric Bayesian filtering method for a certain class of discrete-time nonlinear stochastic systems. The prior distribution and the predictive distribution of the output can be non-Gaussian, while the posterior distribution is approximated by a Gaussian distribution. The mean and variance of the posterior distribution are then regarded as functions of the mean and variance at a previous time step, a known input, and an observed output. A set of linear partial differential equations (PDEs) satisfied by these functions is computed by using algorithms for ideals in rings of differential operators offline, and then the set of linear PDEs is numerically solved online to obtain the mean and variance of the current posterior distribution. A numerical example is provided to show the efficiency of the proposed method.

Keywords: Optimization algorithms, Optimal control, Numerical algorithms
Abstract: We present a numerical method for the minimization of objectives that are augmented with large quadratic penalties of overdetermined inconsistent equality constraints. Such objectives arise from quadratic integral penalty methods for the direct transcription of equality constrained optimal control problems. The Augmented Lagrangian Method (ALM) has a number of advantages over the Quadratic Penalty Method (QPM) for solving this class of problems. However, if the equality constraints of the discretization are inconsistent, then ALM might not converge to a point that minimizes the unconstrained bias of the objective and penalty term. Therefore, in this paper we explore a modification of ALM that fits our purpose. Numerical experiments demonstrate that the modified ALM can minimize certain quadratic penalty-augmented functions faster than QPM, whereas the unmodified ALM converges to a minimizer of a significantly different problem.

Keywords: Optimization algorithms, Optimization, Numerical algorithms
Abstract: In this paper, we propose new proximal Newton-type methods for convex optimization problems in composite form. The applications include model predictive control (MPC) and embedded MPC. Our new methods are computationally attractive since they do not require evaluating the Hessian at each iteration while keeping fast convergence rate. More specifically, we prove the global convergence is guaranteed and the superlinear convergence is achieved in the vicinity of an optimal solution. We also develop several practical variants by incorporating quasi-Newton and inexact subproblem solving schemes and provide theoretical guarantee for them under certain conditions. Experimental results on real-world datasets demonstrate the effectiveness and efficiency of new methods.

Keywords: Optimization algorithms, Optimization, Robust control
Abstract: For a class of nonsmooth composite optimization problems with linear equality constraints, we utilize a Lyapunov-based approach to establish the global exponential stability of the primal-dual gradient flow dynamics based on the proximal augmented Lagrangian. The result holds when the differentiable part of the objective function is strongly convex with a Lipschitz continuous gradient; the non-differentiable part is proper, lower semi-continuous, and convex; and the matrix in the linear constraint is full row rank. Our quadratic Lyapunov function generalizes recent result from strongly convex problems with either affine equality or inequality constraints to a broader class of composite optimization problems with nonsmooth regularizers and it provides a worst-case lower bound of the exponential decay rate. Finally, we use computational experiments to demonstrate that our convergence rate estimate is less conservative than the existing alternatives.

Keywords: Optimization, Optimization algorithms, Computational methods
Abstract: Submodularity is a pivotal property of functions defined on lattices, as it permits their exact minimization and approximate maximization in polynomial time. In this work, we examine submodular function minimization defined on continuous and discrete lattices simultaneously. We identify a class of these mixed optimization problems that can be exactly solved by applying a combination of submodular and convex optimization routines. The utility of this approach is demonstrated via several examples from the proposed class of optimization problems.

Keywords: Optimization algorithms, Optimization
Abstract: This paper develops a heuristic relaxation and iterative search combined algorithm to search for a local optimum of the nonconvex mixed-integer quadratically constrained quadratic programming (MIQCQP) problem. Inspired by the branch and bound method, a heuristic relaxation approach is proposed to relax a MIQCQP problem as a mixed-binary QCQP problem that can be equivalently converted into a continuous/general QCQP. Next, to efficiently solve a general QCQP, an iterative optimization algorithm combined with an intersection cutting plane method is developed, where each iteration is formulated as a second-order cone programming problem. The proposed algorithm will guarantee global convergence to a local optimum of the original MIQCQP problem. Numerical examples are provided and compared to the state-of-the-art method to verify the effectiveness and efficiency of the proposed algorithm.

Keywords: Markov processes, Stochastic systems, LMIs
Abstract: In this paper, we propose a new bounded real lemma (BRL) for discrete-time jump descriptor systems (DJDSs). While the existing studies consider the sufficient condition for the BRL of DJDSs, this paper successfully suggests the necessary and sufficient condition for the BRL of DJDSs. To hold the necessity and sufficiency in terms of linear matrix inequality, two slack variables are introduced by coupling the variables and matrix in the null-space of the singular matrix in DJDSs. A numerical example is provided to show the validity of the result.

Keywords: Information theory and control, Stochastic optimal control, Markov processes
Abstract: Optimal zero-delay coding (fixed-rate quantization) of mathbb{R}^d-valued linear Markov sources is studied. The structure and existence of deterministic and stationary coding policies for the infinite horizon average cost problem is established. Prior results in the literature studying optimality results for Markov sources under infinite horizons either considered finite alphabet sources or, for mathbb{R}^d-valued case, only established the existence of deterministic and non-stationary Markov coding policies or those which are randomized. In addition to existence results, the finite blocklength (time horizon) performance of an optimal (stationary and Markov) coding policy is shown to approach the infinite time horizon optimum at a rate O(1/T).

Keywords: Switched systems, Filtering, Markov processes
Abstract: In this paper we make further foray on the filtering problem for hidden Markov chain, as described in (2). Previous result in the literature on this problem has been obtained in [1], which has derived an optimal nonlinear filter for this problem. The main contribution of this paper is to devise an optimal linear filter for the Markov chain in conjunction with an associated stationary linear filter which amounts here to obtain the convergence of the error covariance matrix. The optimal linear filter derived here bears the following advantages when compared with the one derived in [1]: (i) The innovation coefficients do not depend upon the estimates, which provides a desirable feature of the Kalman filter; (ii) It allows us to derive a stationary filter which has the advantage that it is easy to implement since this filter gain can be performed offline, leading to a linear time-invariant filter. In addition, relying on Euler-Murayama’s stochastic numerical method and the results in [2], we carry out a simulation which shows that the filter performs very well.

Keywords: Hybrid systems, Stability of hybrid systems, Markov processes
Abstract: This work discusses the finite-time asynchronous H-infinity control problem for Markov jump systems in the presence of phenomena that the mode information is hidden and there may exist inaccuracies in controller gains. The hidden mode information is estimated by an hidden Markov model with time-varying mode detection probabilities. Based on the finite-time stability theory and the hidden Markov model based approach, two criteria are provided for analyzing the finite-time H-infinity performance of the considered system and the corresponding finite-time asynchronous H-infinity controller design method is developed. Finally, the theoretical results are verified by a numerical example.

Keywords: Reduced order modeling, Markov processes, Stochastic systems
Abstract: The order of a hidden Markov model (HMM) is an index of the complexity and is closely related to the reachable subspace in the state of the model. When the reachable subspace is not the whole space, there exists a reduced-order quasi hidden Markov model (quasi-HMM), which may not satisfy the nonnegative constraints, equivalent to the original HMM. Such an HMM will be called reachable-space reducible. In this paper, we explore a necessary and sufficient condition for the reachable-space reducible HMM. The condition indicates that if the transition matrix and the observation matrix jointly have a certain structured non-zero pattern, then the HMM is reachable-space reducible. We show that the connection graph of the HMM characterizes the condition. Subsequently, we prove that the HMM satisfying this particular structure always has a reduced-order HMM realization satisfying the nonnegative constraints. Some examples are given to demonstrate our results.

Keywords: Agents-based systems, Optimization, Decentralized control
Abstract: The aim of decentralized gradient descent (DGD) is to minimize a sum of n functions held by interconnected agents. We study the stability of DGD in open contexts where agents can join or leave the system, resulting each time in the addition or the removal of their function from the global objective. Assuming all functions are smooth strongly convex and their minimizers all lie in a given ball, we characterize the sensitivity of the global minimizer of the sum of these functions to the removal or addition of a new function and provide bounds in O(min(κ^1/2, κ/n^1/2,κ^3/2/n)) where κ is the condition number. We also show that the states of all agents can be eventually bounded independently of the sequence of arrivals and departures. The magnitude of the bound scales with the importance of the interconnection, which also determines the accuracy of the final solution in the absence of arrival and departure, exposing thus a potential trade-off between accuracy and sensitivity. Our analysis relies on the formulation of DGD as gradient descent on an auxiliary function. The tightness of our results is analyzed using the PESTO Toolbox.

Keywords: Hybrid systems, Optimization algorithms, Networked control systems
Abstract: In this paper, we present a new class of accelerated distributed algorithms for the robust solution of convex optimization problems over networks. In particular, we propose a novel distributed restarting mechanism for accelerated optimization dynamics with individual asynchronous and periodic time-varying coefficients. Since the algorithms combine continuous-time dynamics with acceleration and discrete-time dynamics, we model the algorithms as well-posed set-valued hybrid dynamical systems. For these dynamics, graph-dependent restarting conditions are derived to establish suitable stability, convergence, and robustness properties for problems characterized by strongly convex, and smooth or non-smooth primal functions. Our results are illustrated via numerical examples.

Keywords: Optimization algorithms, Statistical learning, Markov processes
Abstract: This paper presents a finite time convergence analysis for a decentralized stochastic approximation (SA) scheme. The scheme generalizes several algorithms for decentralized machine learning and multi-agent reinforcement learning. Our proof technique involves separating the iterates into their respective consensual parts and consensus error. The consensus error is bounded in terms of the stationarity of the consensual part, while the updates of the consensual part can be analyzed as a perturbed SA scheme. Under the Markovian noise and time varying communication graph assumptions, the decentralized SA scheme has an expected convergence rate of {cal O}(log T/ sqrt{T} ), where T is the iteration number, in terms of squared norms of gradient for nonlinear SA with smooth but non-convex cost function. This rate is comparable to the best known performances of SA in a centralized setting with a non-convex potential function.

Keywords: Agents-based systems, Cooperative control, Optimization algorithms
Abstract: This paper studies the fixed point finding problem for a global operator over a directed and unbalanced multiagent network, where the global quasi-nonexpansive operator is sum separable and composed of a family of local operators. In this problem, each local operator is privately known to only each individual agent, and all local operators are assumed to be Lipschitz continuous. To deal with this problem, a distributed (or decentralized) algorithm, called Distributed quasi-averaged Operator Tracking algorithm (DOT), is proposed and rigorously analyzed, and it is shown that the algorithm can converge to a fixed point of the global operator at a linear (or exponential) rate under a bounded linear regularity condition, which is strictly weaker than the function’s strong convexity in convex optimization. To validate the proposed algorithm, a numerical example is provided finally.

Keywords: Game theory, Optimization algorithms, Networked control systems
Abstract: We design a distributed algorithm for learning Nash equilibria over time-varying communication networks in a partial-decision information scenario, where each agent can access its own cost function and local feasible set, but can only observe the actions of some neighbors. Our algorithm is based on projected pseudo-gradient dynamics, augmented with consensual terms. Under strong monotonicity and Lipschitz continuity of the game mapping, we provide a very simple proof of linear convergence, based on a contractivity property of the iterates. Compared to similar solutions proposed in literature, we also allow for a time-varying communication and derive tighter bounds on the step sizes that ensure convergence. In fact, in our numerical simulations, our algorithm outperforms the existing gradient-based methods, when the step sizes are set to their theoretical upper bounds. Finally, to relax the assumptions on the network structure, we propose a different pseudo-gradient algorithm, which is guaranteed to converge on time-varying balanced directed graphs.

Keywords: Network analysis and control, Identification, Markov processes
Abstract: We consider a community detection problem for gossip dynamics with stubborn agents in this paper. It is assumed that the communication probability matrix for agent pairs has a block structure. More specifically, we assume that the network can be divided into two communities, and the communication probability of two agents depends on whether they are in the same community. Stability of the model is investigated, and expectation of stationary distribution is characterized, indicating under the block assumption, the stationary behaviors of agents in the same community are similar. It is also shown that agents in different communities display distinct behaviors if and only if state averages of stubborn agents in different communities are not identical. A community detection algorithm is then proposed to recover community structure and to estimate communication probability parameters. It is verified that the community detection part converges in finite time, and the parameter estimation part converges almost surely. Simulations are given to illustrate algorithm performance.

Keywords: Decentralized control, Stochastic optimal control, Stochastic systems
Abstract: This paper considers a nonlinear mean field social optimization problem which aims to minimize a social cost. By use of a finite player model, we apply dynamic programming to formalize a person-by-person (PbP) optimality condition in a feedback form. This procedure leads to a new Hamilton-Jacobi-Bellman equation which involves differentiation with respect to probability measure and is called the master equation of social optimization. For the linear-quadratic (LQ) case, an explicit solution of the master equation is obtained.

Keywords: Networked control systems, Control applications, Optimal control
Abstract: In this paper, we study the global convergence of model-based and model-free policy gradient descent and natural policy gradient descent algorithms for linear quadratic deep structured teams. In such systems, agents are partitioned into a few sub-populations wherein the agents in each sub-population are coupled in the dynamics and cost function through a set of linear regressions of the states and actions of all agents. Every agent observes its local state and the linear regressions of states, called deep states. For a sufficiently small risk factor and/or sufficiently large population, we prove that model-based policy gradient methods globally converge to the optimal solution. Given an arbitrary number of agents, we develop model-free policy gradient and natural policy gradient algorithms for the special case of risk-neutral cost function. The proposed algorithms are scalable with respect to the number of agents due to the fact that the dimension of their policy space is independent of the number of agents in each sub-population. Simulations are provided to verify the theoretical results.

Keywords: Networked control systems, Network analysis and control, Agents-based systems
Abstract: We study non-Bayesian social learning on time-varying directed graphs and show that under mild assumptions on the agents’ prior beliefs and observation structures, all the agents almost surely learn the true state of the world asymptotically in time if the sequence of the associated weighted adjacency matrices belongs to Class P* (a broad class of stochastic chains that subsumes uniformly strongly connected chains), and if certain periods of network connectivity called gamma-epochs occur infinitely often. We argue that this connectivity assumption is weaker and hence more realistic than the popular assumption of uniform strong connectivity. On the other hand, we show that the latter is sufficient to ensure that all the agents’ beliefs converge to a consensus almost surely even when the true state is not identifiable. In addition, we provide a few corollaries of our main result, including two known results on non-Bayesian learning on time-varying graphs. We also show by proof and an example that if the network of influences is balanced in a certain sense, then asymptotic learning occurs almost surely.

Keywords: Reduced order modeling, Learning, Algebraic/geometric methods
Abstract: This paper describes the formulation and experimental testing of a method to estimate submanifold models of animal motion. It is assumed that the animal motion is supported on a configuration manifold,Q, and that the manifold is homeomorphic to a known smooth, Riemannian manifold, S. Estimation of the configuration submanifold is achieved by approximating an unknown mapping from S to Q. The overall problem is cast as a distribution-free learning problem over the manifold of measurements. This paper introduces linear approximation spaces in L²(S) in that contain approximations of the unknown mapping corresponding to those known for classical distribution-free learning theory over Euclidean space. This paper concludes with a study and discussion of the performance of the proposed method using samples from recent reptile motion studies.

Keywords: Neural networks, Optimal control, Predictive control for linear systems
Abstract: Neural networks can be used as approximations of several complex control schemes such as model predictive control. We show in this paper which properties deep neural networks with rectifier linear units as activation functions need to satisfy to guarantee constraint satisfaction and asymptotic stability of the closed-loop system. To do so, we introduce a parametric description of the neural network controller and use a mixed-integer linear programming formulation to perform output range analysis of neural networks. We also propose a novel method to modify a neural network controller such that it performs optimally in the LQR sense in a region surrounding the equilibrium. The proposed method enables the analysis and design of neural network controllers with formal safety guarantees as we illustrate with simulation results.

Keywords: Predictive control for nonlinear systems, Constrained control, Identification for control
Abstract: In this paper, we present a direct data-driven approach to synthesize model reference controllers for constrained nonlinear dynamical systems. To this aim, we employ a hierarchical structure composed by a receding-horizon reference governor and a data-driven low-level controller. Unlike existing approaches, here we jointly design the two blocks by solving a single optimization task, exploiting the fact that the inner controller will never be used alone. The performance of the proposed method is assessed by means of two simulation examples, involving the control of two highly nonlinear benchmark systems.

Keywords: Learning, Machine learning, Optimization
Abstract: This paper proposes a technique for synthesizing smooth nonlinear controllers by optimal policy search and stochastic gradient descent. After choosing an appropriate parameterization of the control law, mini-batch stochastic gradient descent steps are used to iteratively optimize the parameters of the control law. The gradients of the expected future closed-loop performance required for the descent are approximated by using simple local linear models, as introduced earlier by the authors for optimal policy search of linear feedback controllers. In this way, the method does not require a full nonlinear model of the process. The algorithm can be applied offline, on a previously collected dataset, or online, while controlling the plant itself with the most updated policy. We apply the method in a numerical example in which we solve an output-tracking problem for a Continuously Stirred Tank Reactor (CSTR) using a neural-network parameterization with differentiable activation function of the controller. In the offline setting the performance of the resulting neural controller is compared to the one of a linear feedback controller trained on the same dataset. In the online setting, instead, we show how the learning procedure can be designed, combining on-policy and off-policy learning, to increase safety and improve performance.

Keywords: Machine learning, Feedback linearization, Uncertain systems
Abstract: When first principle models cannot be derived due to the complexity of the real system, data-driven methods allow us to build models from system observations. As these models are employed in learning-based control, the quality of the data plays a crucial role for the performance of the resulting control law. Nevertheless, there hardly exist measures for assessing training data sets, and the impact of the spatial distribution of the data on the closed-loop system properties is largely unknown. This paper derives - based on Gaussian process models - an analytical relationship between the density of the training data and the control performance. We formulate a quality measure for the data set, which we refer to as ρ-gap, and derive the ultimate bound for the tracking error under consideration of the model uncertainty. We show how the ρ-gap can be applied to a feedback linearizing control law and provide numerical illustrations for our approach.

Keywords: Machine learning, Robotics
Abstract: In the robotics literature, experience transfer has been proposed in different learning-based control frameworks to minimize the costs and risks associated with training robots. While various works have shown the feasibility of transferring prior experience from a source robot to improve or accelerate the learning of a target robot, there are usually no guarantees that experience transfer improves the performance of the target robot. In practice, the efficacy of transferring experience is often not known until it is tested on physical robots. This trial-and-error approach can be extremely unsafe and inefficient. Building on our previous work, in this paper we consider an inverse module transfer learning framework, where the inverse module of a source robot system is transferred to a target robot system to improve its tracking performance on arbitrary trajectories. We derive a theoretical bound on the tracking error when a source inverse module is transferred to the target robot and propose a Bayesian-optimization-based algorithm to estimate this bound from data. We further highlight the asymmetric nature of cross-robot experience transfer that has often been neglected in the literature. We demonstrate our approach in quadrotor tracking experiments and show that we can efficiently guarantee positive transfer on the target robot for tracking randomly generated periodic trajectories.

Keywords: Networked control systems, Lyapunov methods, Hybrid systems
Abstract: We propose a unifying emulation-based design framework for event-triggered control of nonlinear systems that is based on a hybrid small-gain perspective. We show that various existing event-triggered controllers fit the unifying perspective. Moreover, we demonstrate that the flexibility offered by our approach can be used for the development of novel event-triggered schemes and for a systematic modification of existing schemes. Finally, we illustrate via a simulation example that these novel and/or modified event-triggered controllers can lead to a reduction in the required number of transmissions, while still guaranteeing the same stability properties.

Keywords: Discrete event systems, Sampled-data control, Lyapunov methods
Abstract: The efficient utilization of available resources while simultaneously achieving control objectives is a primary motivation in the event-triggered control paradigm. In many modern control applications, one such objective is enforcing the safety of a system. The goal of this paper is to carry out this vision by combining event-triggered and safety-critical control design. We discuss how a direct transcription, in the context of safety, of event-triggered methods for stabilization may result in designs that are not implementable on real hardware due to the lack of a minimum interevent time. We provide an example showing this phenomena and, building on the insight gained, propose an event-triggered control approach via Input-to-State Safe Barrier Functions that achieves safety while ensuring that interevent times are uniformly lower bounded.

Keywords: Hybrid systems, Formal Verification/Synthesis, Sampled-data control
Abstract: In previous work, linear time-invariant event-triggered control (ETC) systems were abstracted to finite-state systems that capture the original systems' sampling behaviour. It was shown that these abstractions can be employed for scheduling of communication traffic in networks of ETC loops. In this paper, we extend this framework to the class of nonlinear homogeneous systems, however adopting a different approach in a number of steps. Finally, we discuss how the proposed methodology could be extended to general nonlinear systems.

Keywords: Control over communications, Decentralized control, Networked control systems
Abstract: This paper considers decentralized periodic event-triggered control (PETC) for a linear time-invariant plant, composed of spatially distributed sensor and actuator nodes, that are connected by a shared communication channel. The proposed PETC mechanism is based on local trigger rules at the sensor nodes, that use the locally available part of the state error since the last transmission and in addition state information from other sensor nodes that has been transmitted earlier over the communication channel. It is shown how the received information from other sensor nodes can be exploited to reduce the amount of transmissions and to guarantee asymptotic stability of the origin for the closed-loop system with the proposed PETC mechanism. To achieve this, the trigger rules are used to overapproximate a Lyapunov-like function. Moreover, it is demonstrated how the information exploiting PETC mechanism can be modified to deal with network induced transmission delays and bounded state disturbances.

Keywords: Constrained control, Linear systems, Optimal control
Abstract: Minimum attention control proposed by Brockett is an important formulation for resource-aware control, while his problem formulation and the underlying optimization problem that he proposed is in general very hard. In this paper, we propose a computationally tractable design method of minimum attention control based on promoting sparsity of the derivative of control. The optimal control problem is formulated as L0 norm minimization of the time derivative of control under the constraint that the derivative is bounded by a fixed value. This is a non-convex problem, and we propose L1 relaxation for linear systems to obtain optimal control by efficient numerical computation. We then show equivalence theorems between the L0 and L1 optimal controls. Also, we present an example of feedback control for the first-order integrator, that illustrates the proposed methodology.

Keywords: Attack Detection, Fault tolerant systems, Distributed control
Abstract: A problem of attack detection and state estimation in continuous time distributed observer system under combination attack which is defined as in the presence of measurement attack and observer communication attack is considered in this paper. We adopt the notion of virtual state to design an algorithm for attack detection. The algorithm is distributedly used in each local observer and does not need non-local information, thus it can be run by only itself. Additionally, we derive the inequality relationship between system graph connectivity and the number of allowable attacked observers to achieve the detection and estimation with the proposed algorithm as a necessary and sufficient condition. A simple numerical example, finally, illustrates the effectiveness of the proposed algorithm.

Keywords: Networked control systems, Fault detection, Stochastic systems
Abstract: This paper considers a sensor attack and fault detection problem for linear cyber-physical systems, which are subject to system noise that can obey an unknown light-tailed distribution. We propose a new threshold-based detection mechanism that employs the Wasserstein metric, and which guarantees system performance with high confidence with a finite number of measurements. The proposed detector may generate false alarms with a rate ∆ in normal operation, where ∆ can be tuned to be arbitrarily small by means of a benchmark distribution. Thus, the proposed detector is sensitive to sensor attacks and faults which have a statistical behavior that is different from that of the system noise. We quantify the impact of stealthy attacks on open-loop stable systems—which perturb the system operation while producing false alarms consistent with the natural system noise—via a probabilistic reachable set. Tractable implementation is enabled via a linear optimization to compute the detection measure and a semidefinite program to bound the reachable set.

Keywords: Agents-based systems, Attack Detection, Optimization
Abstract: Motivated by the study of deceptive strategies, this paper considers the problems of detecting an agent's objective from its partial path and determining an optimal environment to enable such detection. We focus on a scenario where the agent's objective is to reach a particular target state from a set of potential targets, while an observer seeks to correctly identify such a state prior to the agent reaching it. In order to quantify the predictability of the agent's target given the observed path, we introduce the notion of target entropy, where higher entropy implies lower target predictability. The problem of optimal environment design, i.e., optimal target placement, then becomes a minimax problem with target entropy as an objective function. Under the assumption that the agent chooses its path towards its target maximally unpredictably, we consider models of the agent's motion on both discrete and continuous state spaces. Using dynamic programming, we establish a simple way of computing target entropy for the discrete state space. In a continuous state space, we obtain a formula for target entropy by employing geometrical arguments on volumes of hypersimplices. Additionally, we provide an algorithm yielding an optimal environment in a discrete state space, discuss its computational complexity, and provide a computationally simpler approximation that yields a locally optimal environment. We validate our results on a previously developed model of deceptive agent motion.

Keywords: Estimation, Attack Detection, Large-scale systems
Abstract: The paper develops a distributed filtering methodology for detection of recalcitrant filter nodes. We revisit the discrete time distributed filtering problem and introduce a distributed filter for detecting biasing behavior of such nodes. The nodes of the proposed filter treat the neighbors' information as additional noisy measurements. Also, the network topology is allowed to be time-varying. The calculation of the detector gains involves a matrix recursion and can be carried out on-line.

Keywords: Attack Detection, Distributed control, Predictive control for nonlinear systems
Abstract: Many autonomous control systems are frequently exposed to attacks, so methods for attack identification are crucial for a safe operation. To preserve the privacy of the subsystems and achieve scalability in large-scale systems, identification algorithms should not require global model knowledge. We analyze a previously presented method for hierarchical attack identification, that is embedded in a distributed control setup for systems of systems with coupled nonlinear dynamics. It is based on the exchange of local sensitivity information and ideas from sparse signal recovery. In this paper, we prove sufficient conditions under which the method is guaranteed to identify all components affected by some unknown attack. Even though a general class of nonlinear dynamic systems is considered, our rigorous theoretical guarantees are applicable to practically relevant examples, which is underlined by numerical experiments with the IEEE 30 bus power system.