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When discrete-time Markov jump linear systems are prone to the damaging effects of polytopic uncertainties, it is necessary to address all the vertices of each Markov mode in order to properly design robust controllers. To this end, we propose a robust recursive linear–quadratic regulator for this class of systems. We define a quadratic min–max optimization problem by combining least-squares and penalty functions in a unified framework. We design a one-step cost function to encompass the entire set of vertices of each mode altogether, while maintaining its quadratic structure and the convexity of the problem. The solution is then obtained recursively and does not require numerical optimization packages. We establish conditions for convergence and stability by extending the matrix structure of the recursive solution. In addition, we provide numerical and real-world application examples to validate our method and to emphasize recursiveness and diminished computational effort. [ABSTRACT FROM AUTHOR]

This article investigates the robust cooperative output regulation problem of heterogeneous uncertain linear multiagent systems with switching topologies and infinite distributed communication delays. A novel distributed observer is proposed for each agent to estimate the state of the so-called exosystem by taking consideration of both switching topologies and infinite distributed communication delays. A distributed output feedback controller is then developed based on the internal model principle and the estimated state without using the prior knowledge of communication delays. It is shown via the newly developed Lyapunov-like method that the robust cooperative output regulation problem can be solved under some mild assumptions. Finally, a numerical example is given to demonstrate the effectiveness of the proposed controller. [ABSTRACT FROM AUTHOR]

This article is devoted to the problem of detectability of a large class of linear stochastic systems with time varying coefficients simultaneously affected by state multiplicative white noise perturbations and Markovian switching. The main contribution of this article is to propose a Popov–Belevich–Hautus-type test, which is equivalent to the detectability of the considered stochastic systems in the sense that all unstable modes produce some nonzero output. The proposed setting unifies in some sense the discrete-time and continuous-time ones, dissimilarly to the vast majority of existing works that study discrete and continuous time separately. [ABSTRACT FROM AUTHOR]

This article presents conditions to assure the mean-square stability of linear parameter-varying systems with Markov jumps. The model dynamics are driven not only by a Markov chain but also by time-varying parameters that take values in a polytopic set. No assumption is imposed on how the parameters vary within the polytopic set, i.e., the variation rate can be arbitrarily fast. The proposed conditions stem from a homogeneous polynomial Lyapunov function in the state space, adapted to account for Markov jumps. The stability certificate is sought through linear matrix inequalities. Numerical examples illustrate this article’s contribution. [ABSTRACT FROM AUTHOR]

In this article, a novel set-membership state estimation method based on zonotopes is proposed for switched systems subject to unknown-but-bounded disturbance with average dwell time (ADT) switching. By testing the consistency between the system model and measured output, an intersection zonotope is constructed based on mode-dependent and semitime-dependent correction matrix. Then, by constructing semitime-dependent $P$ -radius functions, the issue of $L_{\infty }$ disturbance attenuation performance for the intersection zonotope is addressed. Finally, a numerical example is presented to illustrate the effectiveness of the proposed approach. [ABSTRACT FROM AUTHOR]

This article develops the sliding mode control (SMC) strategy for linear impulsive systems with matched disturbances. Such systems describe dynamical systems that evolve according to continuous process most of the time with matched disturbances, but instantaneously exhibit discontinuities, i.e., impulsive disturbances. A suitable sliding surface function is proposed and the resulting sliding mode dynamics are a class of linear impulsive systems. Some sufficient conditions coupled with impulse time sequences are proposed to guarantee the reachability of the predesigned sliding surface and the stability of the reduced-order impulsive systems under sliding motion, respectively. We show how restrictions on the structure of the systems and impulses should be imposed to ensure the feasibility of the proposed SMC strategy in comparison with general SMC in continuous space. To show the effectiveness of the proposed approach, two simulation examples are presented at the end. [ABSTRACT FROM AUTHOR]

This article considers linear discrete-time systems with additive disturbances and designs a model predictive control (MPC) law incorporating a dynamic feedback gain to minimize a quadratic cost function subject to a single chance constraint. The feedback gain is selected online, and we provide two selection methods based on minimizing upper bounds on predicted costs. The chance constraint is defined as a discounted sum of violation probabilities on an infinite horizon. By penalizing violation probabilities close to the initial time and assigning violation probabilities in the far future with vanishingly small weights, this form of constraints allows for an MPC law with guarantees of recursive feasibility without a boundedness assumption on the disturbance. A computationally convenient MPC optimization problem is formulated using Chebyshev’s inequality, and we introduce an online constraint-tightening technique to ensure recursive feasibility. The closed-loop system is guaranteed to satisfy the chance constraint and a quadratic stability condition. With dynamic feedback gain selection, the closed-loop cost is reduced and conservativeness of Chebyshev’s inequality is mitigated. Also, a larger feasible set of initial conditions can be obtained. Numerical simulations are given to show these results. [ABSTRACT FROM AUTHOR]

Observability of a hybrid system is defined as the ability to determine the continuous state of the system. Whether a hybrid system is observable or not depends on which events can be disabled, which events can be forced, and the connectivity of the discrete states, as well as its continuous dynamics. We model a hybrid system using a hybrid machine that takes into consideration both continuous variables and discrete events. We classify hybrid systems into four classes based on their discrete-event parts. For each class, conditions are derived to check observability. If a hybrid system is not observable, then we check if a weaker version of observability, called $B$ -observability, is satisfied. $B$ -observability requires that a hybrid system become observable after some finite occurrences of events. Conditions are derived to check $B$ -observability. These conditions involve both the discrete-event and continuous-variable parts of hybrid systems. If the continuous-variable part of a system has a constant- $A$ matrix, then the conditions for the continuous-variable part can be simplified. We illustrate the results by an example of a battery management system of an electric vehicle. [ABSTRACT FROM AUTHOR]

This article investigates the problem of how to control nonlinear systems with delays in the state by memoryless linear feedback. The notions of semiglobal asymptotic stabilization and sublevel sets are introduced in the context of time-delay systems. With the aid of Razumikhin theorem, we develop a semiglobal design method for the construction of Lyapunov functions, associated sublevel sets, and delay-free linear state feedback laws, step-by-step, achieving semiglobal asymptotic stabilization for time-delay nonlinear systems in a lower triangular form. In contrast to the global stabilization of nonlinear systems with delays in the state, which is usually achieved by dynamic state feedback (Lin and Zhang, 2020), the significance of this work is to point out that a tradeoff of the control objectives, e.g., semiglobal versus global stabilization, makes it possible to control a class of time-delay nonlinear systems by static linear feedback. Extensions to nonlinear systems with globally asymptotically locally expoentially stable (GALES)-like inverse dynamics are also included in this article. [ABSTRACT FROM AUTHOR]

In this article, we aim at developing computationally tractable methods for nonlinear model/controller reduction. Recently, model reduction by generalized differential (GD) balancing has been proposed for nonlinear systems with constant input-vector fields and linear output functions. First, we study incremental properties in the GD balancing framework. Next, based on these analyses, we provide GD linear quadratic Gaussian (LQG) balancing and GD $H_\infty$ -balancing as controller reduction methods for nonlinear systems by focusing on linear feedback and observer gains. Especially for GD $H_\infty$ -balancing, we clarify when the closed-loop system consisting of the full-order system and a reduced-order controller is exponentially stable. All provided methods for controller reduction can be relaxed to linear matrix inequalities (LMIs). [ABSTRACT FROM AUTHOR]

Group consensus implies reaching multiple groups where agents belonging to the same cluster reach state consensus. This article focuses on linear multiagent systems under nonnegative directed graphs. A new necessary and sufficient condition for ensuring group consensus is derived, which requires the spanning forest of the underlying directed graph and that of its quotient graph induced with respect to a clustering partition to contain equal minimum number of directed trees. This condition is further shown to be equivalent to containing cluster spanning trees, a commonly used topology for the underlying graph in the literature. Under a designed controller gain, lower bound of the overall coupling strength for achieving group consensus is specified. Moreover, the pattern of the multiple consensus states formed by all clusters is characterized when the overall coupling strength is large enough. [ABSTRACT FROM AUTHOR]

Two stochastic model predictive control algorithms, which are referred to as distributionally robust model predictive control algorithms, are proposed in this article for a class of discrete linear systems with unbounded noise. Participially, chance constraints are imposed on both of the state and the control, which makes the problem more challenging. Inspired by the ideas from distributionally robust optimization (DRO), two deterministic convex reformulations are proposed for tackling the chance constraints. Rigorous computational complexity analysis is carried out to compare the two proposed algorithms with the existing methods. Recursive feasibility and convergence are proven. Simulation results are provided to show the effectiveness of the proposed algorithms. [ABSTRACT FROM AUTHOR]

Ensuring safety is crucial for the successful deployment of autonomous systems, such as self-driving vehicles, unmanned aerial vehicles, and robots acting close to humans. While there exist many controllers that optimize certain criteria, such as energy consumption, comfort, or low wear, they are usually not able to guarantee safety at all times for constrained nonlinear systems affected by disturbances. Many controllers providing safety guarantees, however, have no optimal performance. The idea of this article is, therefore, to synthesize a formally correct controller that serves as a safety net for an unverified, optimal controller. This way, most of the time, the optimal controller is in charge and leads to a desired, optimal control performance. The safety controller constantly monitors the actions of the optimal controller and takes over if the system would become unsafe. The safety controller utilizes a novel concept of backward reachable set computation, where we avoid the need of computing underapproximations of reachable sets. We have further developed a new approach that analytically describes reachable sets, making it possible to efficiently maximize the size of the backward reachable set. We demonstrate our approach by a numerical example from autonomous driving. [ABSTRACT FROM AUTHOR]

We study autocovariance least squares (ALS) estimation methods for covariance estimation for linear time-invariant systems. Previous works have posited that calculation of the ALS weighting matrix is intractable unless the number of data points $N_d$ is small because it requires storage of a matrix whose number of elements scales as $N_d^4$. We derive a novel way to compute the weight that avoids this difficulty. In practice, the true optimal weight cannot be calculated because it is a function of the sought covariance matrices. However, our work enables implementation of two novel ALS algorithms that estimate the weight from data. For the purpose of comparison, we also discuss ALS with an arbitrary weight (such as an identity matrix) and present a previously published method for estimating the ALS weight. ALS with an identity weight guarantees unbiased and consistent covariance estimates, but algorithms that estimate the weight from data do not inherit these guarantees. Despite this drawback, we present a numerical example for which the best performing algorithm, iterative estimation of the covariances and the ALS weight, produces covariance estimates with a small amount of bias and a significantly reduced variance compared to all other algorithms. [ABSTRACT FROM AUTHOR]

We propose a state estimation methodology using a network of distributed observers. We consider a scenario in which the local measurement at each node may not guarantee the system's observability. In contrast, the ensemble of all the measurements does ensure that the observability property holds. As a result, we design a network of observers such that the estimated state vector computed by each observer converges to the system's state vector by using the local measurement and the communicated estimates of a subset of observers in its neighborhood. The proposed estimation scheme exploits sensor redundancy to provide robustness against faults in the sensors. Under suitable conditions on the redundant sensors, we show that it is possible to mitigate the effects of a class of sensor faults on the state estimation. Simulation trials demonstrate the effectiveness of the proposed distributed estimation scheme. [ABSTRACT FROM AUTHOR]

Linear complementarity system (LCS) consists of an ordinary differential equation (ODE) and a linear complementarity problem (LCP). In this article, we propose an exponential time-stepping method for solving LCS, which uses exponential integrator to discretize the ODE and solves the LCPs at the discrete time points. Numerical results are reported for illustrating its good performance. [ABSTRACT FROM AUTHOR]

The goal of this article is to investigate new and simple convergence analysis of dynamic programming for the linear–quadratic regulator problem of discrete-time linear time-invariant systems. In particular, bounds on errors are given in terms of both matrix inequalities and matrix norm. Under a mild assumption on the initial parameter, we prove that the $Q$ -value iteration exponentially converges to the optimal solution. Moreover, a global asymptotic convergence is also presented. These results are then extended to the policy iteration. We prove that in contrast to the $Q$ -value iteration, the policy iteration always converges exponentially fast. An example is given to illustrate the results. [ABSTRACT FROM AUTHOR]

In this article, the finite-time stabilization problem is solved for a linear time-varying system with unknown control direction by exploiting a modified version of the classical extremum-seeking algorithm. We propose to use a suitable oscillatory input to modify the system dynamics, at least in an average sense, so as to satisfy a differential linear matrix inequality condition, which in turn guarantees that the system’s state remains inside a prescribed time-varying hyperellipsoid in the state space. The finite-time stability (FTS) of the averaged dynamics implies the FTS of the original system, as the distance between the original and the averaged dynamics can be made arbitrarily small by choosing a sufficiently high value of the dithering frequency used by the extremum-seeking algorithm. The main advantage of the proposed approach resides in its capability of dealing with systems with unknown control direction, and/or with a control direction that changes over time. Being FTS a quantitative approach, this article also gives an estimate of the necessary minimum dithering/mixing frequency provided, and the effectiveness of the proposed finite-time stabilization approach is analyzed by means of numerical examples. [ABSTRACT FROM AUTHOR]

This article proposes a method for enlarging the region of attraction of linear model predictive controllers (MPC) when tracking piecewise-constant references in the presence of pointwise-in-time constraints. It consists of an add-on unit, the feasibility governor (FG), that manipulates the reference command so as to ensure that the optimal control problem that underlies the MPC-feedback law remains feasible. Offline polyhedral projection algorithms based on multiobjective linear programming are employed to compute the set of feasible states and reference commands. Online, the action of the FG is computed by solving a convex quadratic program. The closed-loop system is shown to satisfy constraints, be asymptotically stable, exhibit zero-offset tracking, and display finite-time convergence of the reference. [ABSTRACT FROM AUTHOR]

The problem of global output tracking is addressed for stable minimum phase systems, with constant uncertain parameters and constant disturbances belonging to a known compact set, in the presence of input constraints such as amplitude saturation. The relative degree, the system order, and the sign of the high frequency gain are assumed to be known. A hybrid adaptive output feedback control is designed to achieve global asymptotic output tracking, provided that there exists an input within the input constraints capable of tracking exactly the output reference signal. By virtue of the hybrid control approach, the closed-loop system is linear within each time interval between parameter updating. Moreover, no information on input saturation is required by the controller. In addition to the standard assumptions in adaptive control design when inputs are unconstrained, further requirements on the reference signals, on system stability and on parameter bounds, are needed when inputs are constrained. [ABSTRACT FROM AUTHOR]

In this article, we study a class of generalized Persidskii systems with external disturbances and establish conditions, in the form of linear matrix inequalities, for input-to-output stability and robust synchronization for these systems. We apply the obtained results to the robust control design for synchronizing linear systems and to the synchronization of Hindmarsh–Rose models of neurons. [ABSTRACT FROM AUTHOR]

We investigate the implementation of a sparsitypromoting hands-off control scheme using the alternating direction method of multiplies (ADMM). In order to minimize the numerical control effort along with the actuation one, only a single ADMM iteration per time step is considered. We analyze the resulting closed-loop dynamics for linear systems with additive disturbances and show that the proposed scheme provides sparse controls as desired and, in addition, ensures input-to-state practical stability. We further point out a close relation between the proposed real-time scheme and (nonminimum time) dead-beat control. Finally, characteristics and effectiveness of the novel hands-off controller(s) are illustrated with numerical examples. [ABSTRACT FROM AUTHOR]

This article addresses the approximate and exact controllability issues of switched infinite-dimensional linear systems. First, a controllability map that is related to switching sequence and a controllability Gramian operator are proposed, based on which two necessary and sufficient conditions are established for approximate and exact controllability, respectively. Second, it shows that the obtained conditions can degenerate into the existing controllability criteria of infinite-dimensional linear systems, switched finite-dimensional linear systems, and a single finite-dimensional linear system. Finally, the new results are applied to analyze the approximate controllability of switched linear parabolic systems and the exact controllability of switched linear wave systems. Two examples are given to illustrate the effectiveness of the proposed approaches. [ABSTRACT FROM AUTHOR]

This article investigates the event-triggered control problem for switched affine systems (SASs). The presence of affine terms brings many difficulties on the exclusion of triggering Zeno behavior when ensuring asymptotic stability. We propose an event-triggered control strategy dynamically updated with triggering to solve this problem, in which the triggering condition is associated with the affine terms and given with a time-varying term that is updated at triggering instants. Based on the triggering strategy, the controllers for subsystems and a switching rule are designed to achieve asymptotic stability of the resulting closed-loop system. Moreover, due to the special feature of event-triggered SASs, a new method for proving the exclusion of Zeno behavior is given. Finally, the developed results are illustrated by an electric circuit example. [ABSTRACT FROM AUTHOR]

In robust control under state constraints, the set of admissible inputs is usually considered as given, under the assumption that the actuators have been already designed. However, if the input set is too small, any controller will fail in stabilizing the closed-loop system while satisfying all prescribed constraints for some initial states of interest, or vice versa the chosen actuators may be oversized. To handle this issue, in this article, we address the problem of computing the smallest input constraint set such that the closed-loop system is stabilizable from a prescribed set of initial states while respecting all constraints. We focus our attention on linear systems with additive disturbances, and develop the algorithm based on recursive feasibility of robust model predictive control. We demonstrate the results using numerical examples, in which we consider different metrics for the input constraint set selection. [ABSTRACT FROM AUTHOR]

The article investigates the problem of estimating the state of a time-varying system with a linear measurement model; in particular, the article considers the case where the number of measurements available can be smaller than the number of states. In lieu of a batch linear least-squares approach—well-suited for static networks, where a sufficient number of measurements could be collected to obtain a full-rank design matrix—the article proposes an online algorithm to estimate the possibly time-varying state by processing measurements as and when available. The design of the algorithm hinges on a generalized least-squares cost augmented with a proximal-point-type regularization. With the solution of the regularized least-squares problem available in closed-form, the online algorithm is written as a linear dynamical system where the state is updated based on the previous estimate and based on the new available measurements. Conditions under which the algorithmic steps are in fact a contractive mapping are shown, and bounds on the estimation error are derived for different noise models. Numerical simulations are provided to corroborate the analytical findings. [ABSTRACT FROM AUTHOR]

Robustness and reliability are two key requirements for developing practical quantum control systems. The purpose of this article is to design a coherent feedback controller for a class of linear quantum systems suffering from Markovian jumping faults so that the closed-loop quantum system has both fault tolerance and $H^\infty$ disturbance attenuation performance. This article first extends the physical realization conditions from the time-invariant case to the time-varying case for linear stochastic quantum systems. By relating the fault-tolerant $H^\infty$ control problem to the dissipation properties and the solutions of Riccati differential equations, an $H^\infty$ controller for the quantum system is then designed by solving a set of linear matrix inequalities. In particular, an algorithm is employed to introduce additional quantum inputs and to construct the corresponding input matrices to ensure the physical realizability of the quantum controller. Also, we propose a real application of the developed fault-tolerant control strategy to quantum optical systems. A linear quantum system example from quantum optics, where the amplitude of the pumping field randomly jumps among different values due to the fault processes, can be modeled as a linear Markovian jumping system. It is demonstrated that a quantum $H^\infty$ controller can be designed and implemented using some basic optical components to achieve the desired control goal for this class of systems. [ABSTRACT FROM AUTHOR]

We propose algorithms for performing model checking and control synthesis for discrete-time uncertain systems under linear temporal logic (LTL) specifications. We construct temporal logic trees (TLTs) from LTL formulae via reachability analysis. In contrast to automaton-based methods, the construction of the TLT is abstraction-free for infinite systems; that is, we do not construct discrete abstractions of the infinite systems. Moreover, for a given transition system and an LTL formula, we prove that there exist both a universal TLT and an existential TLT via minimal and maximal reachability analysis, respectively. We show that the universal TLT is an underapproximation for the LTL formula and the existential TLT is an overapproximation. We provide sufficient conditions and necessary conditions to verify whether a transition system satisfies an LTL formula by using the TLT approximations. As a major contribution of this work, for a controlled transition system and an LTL formula, we prove that a controlled TLT can be constructed from the LTL formula via a control-dependent reachability analysis. Based on the controlled TLT, we design an online control synthesis algorithm, under which a set of feasible control inputs can be generated at each time step. We also prove that this algorithm is recursively feasible. We illustrate the proposed methods for both finite and infinite systems and highlight the generality and online scalability with two simulated examples. [ABSTRACT FROM AUTHOR]

We consider the problem of identifying a dissipative linear model of an unknown nonlinear system that is known to be dissipative, from time-domain input–output data. We first learn an approximate linear model of the nonlinear system using standard system identification techniques and then perturb the system matrices of the linear model to enforce dissipativity, while closely approximating the dynamical behavior of the nonlinear system. Further, we provide an analytical relationship between the size of the perturbation and the radius in which the dissipativity of the linear model guarantees local dissipativity of the unknown nonlinear system. We demonstrate the application of this identification technique through two examples. [ABSTRACT FROM AUTHOR]

This article provides an extension of the observability rank condition to time-varying nonlinear systems. Previous conditions to check the state observability only hold for nonlinear systems that do not explicitly depend on time, or, for time-varying systems, they only account for the linear case. In this article, a general analytic condition is provided. The new condition reduces to the well-known observability rank condition in the two simpler cases of time-varying linear systems and time-invariant nonlinear systems. The proposed condition is applied to aerospace robotics to study the observability of a lunar-module-type system equipped with monocular vision and inertial sensors. [ABSTRACT FROM AUTHOR]

This article is concerned with the distributed Kalman filtering problem for discrete-time linear systems whose measurement information comes from a set of sensor nodes that can communicate with their direct neighbors. Two algorithms for distributed Kalman filtering are proposed, where the first algorithm is based on single-node measurement and the second algorithm is based on neighboring-node measurements. In order to improve the performance, a novel criterion is introduced to the algorithm design, where in the criterion, the proximity of matrix’s trace is used to determine the proximity of positive semidefinite matrix. We prove that all the proposed algorithms for distributed Kalman filtering are unbiased. Numerical examples are provided to demonstrate the correctness of the proposed theoretical method and the performance of the proposed new design technique. [ABSTRACT FROM AUTHOR]

In this article, we present a novel data-driven model predictive control (MPC) approach to control unknown nonlinear systems using only measured input–output data with closed-loop stability guarantees. Our scheme relies on the data-driven system parameterization provided by the fundamental lemma of Willems et al. We use new input–output measurements online to update the data, exploiting local linear approximations of the underlying system. We prove that our MPC scheme, which only requires solving strictly convex quadratic programs online, ensures that the closed loop (practically) converges to the (unknown) optimal reachable equilibrium that tracks a desired output reference while satisfying polytopic input constraints. As intermediate results of independent interest, we extend the fundamental lemma to affine systems and we derive novel robustness bounds w.r.t. noisy data for the open-loop optimal control problem, which are directly transferable to other data-driven MPC schemes in the literature. The applicability of our approach is illustrated with a numerical application to a continuous stirred tank reactor. [ABSTRACT FROM AUTHOR]

In this article, the problem of distributed state estimation for a continuous-time linear system with a sensor network is investigated, where each sensor can only communicate with its neighbors and contains time-correlated measurement noise. To solve this problem, a novel augmented leader-following information fusion strategy is first proposed to collect measurements and system matrices. Then, a class of distributed state estimators is developed with bounded estimation error covariances. Further, a closed-form relation between the designed distributed estimator and the centralized estimator is established. It is found that the estimation performance of the former converges to that of the latter when the consensus gain tends to infinity. The proposed estimator is further extended to the fully distributed case by introducing an adaptive law for the consensus gain without using any global information. Moreover, it is shown that the designed estimator is applicable for systems with deterministic noise. Finally, several comparative numerical simulations are provided to demonstrate the effectiveness and superiority of the theoretical results. [ABSTRACT FROM AUTHOR]

Critical systems must be designed resilient to malfunctions and especially to a loss of control authority over actuators. This malfunction considers actuators producing uncontrolled and possibly undesirable outputs. We investigate the design of resilient linear systems capable of reaching their target even after such a malfunction. In contrast with the settings considered by robust control and fault-tolerant control, we consider undesirable but observable inputs of the same magnitude as controls since they are produced by a faulty actuator belonging to the system. The control inputs can then depend on these undesirable inputs. Building on our previous work, we focus on designing resilient systems able to withstand the loss of one or multiple actuators. Since resilience refers to the existence of a control law driving the state to the target, we naturally continue with the synthesis of such a control law. We conclude with the application of our theory to the ADMIRE-fighter-jet model. [ABSTRACT FROM AUTHOR]

Considering a discrete-time linear parameter-varying systems with input constraints, this article deals with the codesign of a parameter-dependent state-feedback controller and a new parameter-dependent event-triggering mechanism. Two independent event-triggering policies are introduced at the sensor node to economize the limited network resources. They indicate whether the current state or the current scheduling parameters should be transmitted to the controller or not. In this sense, the controller scheduling parameters can differ from those of the system, yielding a certain degree of robustness concerning parameter deviations. Sufficient conditions, given in terms of linear matrix inequalities, ensure the regional asymptotic stability of the closed loop. To formulated them, we use the Lyapunov theory along with the generalized sector condition. Moreover, we formulate a convex optimization procedure indirectly reducing the transmission activity over the network. The proposed methodology effectiveness is attested through numerical examples and comparisons with related works from the literature. [ABSTRACT FROM AUTHOR]

This article investigates the transformation of Hamiltonian structures under sampling. It is shown that the exact sampled equivalent model associated to a given port-Hamiltonian continuous-time dynamics exhibits a discrete-time representation in terms of the discrete gradient, with the same energy function but modified damping and interconnection matrices. By construction, the proposed sampled-data dynamics guarantees exact matching of both the state evolutions and the energy-balance at all sampling instants. Its generalization to port-controlled Hamiltonian dynamics leads to characterize a new power conjugate output so recovering the concept of average passivation. On these bases, energy-management control strategies can be proposed. An energetic interpretation of the approach is confirmed by its formulation in the Dirac formalism. Two classical examples are worked out to validate the proposed sampled-data modeling in a comparative way with the literature. [ABSTRACT FROM AUTHOR]

This article deals with the input–output finite-time stability (IO-FTS) of linear discrete-time systems. In current control science, discrete-time systems play a very important role in many engineering contexts. Moreover, many discrete-time control problems are defined over a finite-interval of time; therefore, the development and application of finite-time control methodologies is of particular relevance. The first contribution of this article is a pair of necessary and sufficient conditions for IO-FTS. The former involves the solution of a set of generalized difference Lyapunov equations; the latter allows one to establish the feasibility of an optimization problem by solving a set of difference linear matrix inequalities (DLMIs). The second contribution of this article is a theorem for IO finite-time stabilization via state feedback, followed by a more general one for stabilization via output feedback. Both conditions are necessary and sufficient, and lead to optimization problems cast in the form of DLMIs. The applicability of the devised results is illustrated through a numerical example. [ABSTRACT FROM AUTHOR]

The discrete distributed observer is developed recently to solve the cooperative output regulation problem. The validation of the existing discrete distributed observer depends on the establishment of the communication network. In some practical applications, only the sensor network can be established among all agents. To handle such cases, we propose a sensory feedback-based discrete distributed observer, which depends on the relative output of neighboring agents. In contrast to existing results, the design of the discrete distributed observer and cooperative output regulation analysis should be conducted simultaneously. Resorting to the small-gain theorem, we develop a small-gain condition-based approach and a low-gain-based approach, respectively. By these two approaches, we demonstrate that the discrete distributed observer holds and the cooperative output regulation problem of heterogeneous discrete-time linear multiagent systems can be solved. [ABSTRACT FROM AUTHOR]

This article investigates the stealthy false data injection attack design problem for a class of cyber physical systems equipped with state estimators and attack detectors. The objective is to worsen the estimation performance without triggering any alarm. First, a necessary and sufficient condition for the existence of perfect attacks, which alter the state estimate without affecting residual signals, is provided. It is shown that the estimation error can be arbitrarily large under the well-designed perfect attacks. Second, if the perfect attacks do not exist, the existence of nonperfect attacks, which worsen the estimation performance with a degree influence on residual signals, is analyzed. It is shown that the desired nonperfect attack sequence can be designed by analyzing the maximum eigenvalue and the corresponding eigenvector of an auxiliary matrix. Compared with the existing methods, in this article, attacks are designed without knowledge of estimators and can be injected from any time point. Finally, a numerical simulation is provided to illustrate the effectiveness of the proposed methods. [ABSTRACT FROM AUTHOR]

This article derives a solution to the appointed-time and attack-free bipartite synchronization problem for generic linear multiagent systems over directed switching networks accommodating cooperative and antagonistic interactions. Herein, appointed-time means that the settling time is independent of any parameters and is preappointed in advance. Attack-free requires that the communication channel is protected, which means that no state and observer information exchange is allowed, and only measured relative output information is available when designing protocols. Firstly, by virtue of Pontryagin’s maximum principle, a distributed appointed-time state-feedback protocol is developed for directed switching networks, which tackles the appointed-time bipartite synchronization problem from a motion-planning approach based on sampling measurements, but takes the risk of facing cyber attacks on information exchange channels. Then, to be free of network attacks, a sampling-based attack-free observer using relative output information is designed to observe bipartite synchronization errors at an appointed time. By combining the appointed-time state-feedback protocol with the sampling-based attack-free observer, an attack-free output-feedback protocol is developed without requiring the state or control input information. The attack-free appointed-time bipartite synchronization problem is thus resolved. Both the state-feedback and attack-free protocols show the ability of disturbance rejection to the nonidentical bounded disturbances. To our knowledge, it is the first time to solve the appointed-time and attack-free bipartite synchronization problem for generic linear multiagents based on state- and output-feedback information, respectively. Finally, simulations verify the effectiveness of the two protocols. [ABSTRACT FROM AUTHOR]

This article aims to improve the stochastic filtering algorithm with bounded disturbances, proposed in 1. This filter is efficient for max-plus linear systems in explicit form, i.e., the timed event graph (TEG) described by this system is initially with one token on each place. Nevertheless, it needs strong assumptions in order to be accurate for systems in implicit form, i.e., the corresponding TEG is initially with some token-free places which implies that some entries of the system state vector are dependent on each other. In this article, we consider a more general method without these assumptions. It is based on an iterative procedure that widely increases the accuracy of the estimation. [ABSTRACT FROM AUTHOR]

This article focuses on the design of online optimal input sequence for robust active fault diagnosis of discrete-time linear parameter-varying systems using set-theoretic methods. Instead of the traditional set-separation constraint conditions leading to the design of offline input sequence, the proposed approach focuses on online (re)shaping of the input sequence based on the real-time information of the output to discriminate system modes at each time instant such that the diagnosability of system has potential to be further improved. The criterion on the design of optimal input is characterized based on a nonconvex fractional programming problem at each time instant, which is shown to be efficiently solved within a convex optimization framework. In addition to this main contribution, by exploiting Lagrange duality, the optimal input is explicitly obtained by solving a characteristic equation. At the end, a physical circuit model is provided to illustrate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

We investigate state estimation of linear systems over channels having a finite state not known by the transmitter or receiver. We show that similar to memoryless channels, zero-error capacity is the right figure of merit for achieving bounded estimation errors. We then consider finite-state, worst-case versions of the common erasure, and additive noise channels models, in which the noise is governed by a finite-state machine without any statistical structure. Upper and lower bounds on their zero-error capacities are derived, revealing a connection with the topological entropy of the channel dynamics. Separate necessary and sufficient conditions for bounded linear state estimation errors via such channels are obtained. These estimation conditions bring together the topological entropies of the linear system and the discrete channel. [ABSTRACT FROM AUTHOR]

In a recent article, we have shown how to learn controllers for unknown linear systems using finite-length noisy data by solving linear matrix inequalities. In this article, we extend this approach to deal with unknown nonlinear polynomial systems by formulating stability certificates in the form of data-dependent sum of squares programs, whose solution directly provides a stabilizing controller and a Lyapunov function. We then derive variations of this result that lead to more advantageous controller designs. The results also reveal connections to the problem of designing a controller starting from a least-square estimate of the polynomial system. [ABSTRACT FROM AUTHOR]

Dissipativity properties have proven to be very valuable for systems analysis and controller design. With the rising amount of available data, there has, therefore, been an increasing interest in determining dissipativity properties from (measured) trajectories directly, while an explicit model of the system remains undisclosed. Most existing approaches for data-driven dissipativity, however, guarantee the dissipativity condition only over a finite-time horizon and provide weak or no guarantees on robustness in the presence of noise. In this article, we present a framework for verifying dissipativity properties from measured data with desirable guarantees. We first consider the case of input-state measurements, where we provide computationally attractive conditions in the presence of process noise. We extend this approach to input–output data, where similar results hold in the noise-free case, and finally provide results for the case of noisy input–output trajectories. [ABSTRACT FROM AUTHOR]

A linear dynamical system is called $k$ -positive if its dynamics maps the set of vectors with up to $k-1$ sign variations to itself. For $k=1$ , this reduces to the important class of positive linear systems. Since stable positive linear time-invariant systems always admit a diagonal quadratic Lyapunov function, i.e., they are diagonally stable, we may expect that this holds also for stable $k$ -positive systems. We show that, in general, this is not the case both in the continuous-time and discrete-time (DT) case. We then focus on DT $k$ -positive linear systems and introduce the new notion of the DT $k$ -diagonal stability. It is shown that this is a necessary condition for the standard DT diagonal stability. We demonstrate an application of this new notion to the analysis of a class of DT nonlinear systems. [ABSTRACT FROM AUTHOR]

In this article,we study the linear time-invariant state-feedback controller design problem for distributed systems. We follow the recently developed system level synthesis (SLS) approach and impose locality structure on the resulting closed-loop mappings; the corresponding controller implementation inherits this prescribed structure. In contrast to existing SLS results, we derive an explicit (rather than implicit) parameterization of all achievable stabilized closed-loops. This admits more efficient IIR representations of the temporal part of the closed-loop dynamics, and it allows for the $\mathcal {H}_2$ design problem with closed-loop spatial sparsity constraints to be converted to a standard model matching problem, with the number of transfer function parameters scaling linearly with the closed-loop spatial extent constraint. We illustrate our results with two applications: consensus of first-order subsystems and the vehicular platoons problem. In the case of first-order consensus, we provide analytic solutions and further analyze the architecture of the resulting controller implementation. Results for infinite extent spatially invariant systems are presented to provide insight to the case of a large but finite number of subsystems. [ABSTRACT FROM AUTHOR]

The Battistelli–Hespanha–Mosca–Tesi (BHMT) adaptive reset switching algorithm is enhanced to admit bumpless transfer and to control a nonlinear time-varying plant using the broad class of two-degree-of-freedom nonlinear time-varying controllers. Performance, including stability and exponential stability, is proved given only that the adaptive stabilization problem is $\lambda$ -feasible, which means at every time, there exists at least one exponentially stabilizing controller. We relax two restrictive BHMT assumptions: i) the plant is linear time-invariant (LTI) over most intervals and has finite order and ii) each controller is LTI. And, we expand the scope to include a broad class of bumpless switching algorithms. An example is provided to support the improved results. [ABSTRACT FROM AUTHOR]

In this article, a noisy-output-based direct learning tracking control is proposed for stochastic linear systems with nonuniform trial lengths. The iteration-varying trial length is modeled using a Markov chain for demonstration of the iteration dependence. The effect of the noisy output is asymptotically eliminated using a prior given decreasing gain sequence in the learning algorithm. Two alternative adaptive gains are presented for improving the tracking performance and the convergence speed. Both the mean-square and almost-sure convergence are provided. Numerical simulations on a four-degree-of-freedom robot arm are presented to illustrate the effectiveness of the proposed scheme. [ABSTRACT FROM AUTHOR]

A structured preconditioned conjugate gradient (PCG) based solver is developed for implementing the Newton updates in second-order methods for a class of constrained network optimal control problems. Of specific interest are problems with discrete-time dynamics arising from the path-graph interconnection of $N$ heterogeneous subsystems. The arithmetic complexity of each PCG step is $O(NT)$ , where $T$ is the length of the time horizon. The proposed preconditioning involves a fixed number of block Jacobi iterations per PCG step. A decreasing analytic bound on the effective conditioning is given in terms of this number. The associated computations are decomposable across the spatial and temporal dimensions of the optimal control problem, into subproblems of size independent of $N$ and $T$. Numerical results are provided for two example systems. [ABSTRACT FROM AUTHOR]