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Set theoretic analysis plays a crucial part in understanding safety requirements for control systems. We apply the lattice theoretic insights of fixed point theorems to construct the maximal invariant set and verify safety constraint satisfaction. We present a Kleene iteration-based algorithm with a novel initialization—based on omega-limit sets—for exactly computing the maximal invariant set under

In the article entitled “Distributed synthesis of local controllers for networked systems with arbitrary interconnection topologies” published in the IEEE Transactions on Automatic Control , vol. 66, pp. 683–698, 2021, there were some missing terms in Lemma 1 and the definition of the messenger matrices. Here, we include these terms and suitably modify the corresponding proofs. Note that all the main

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This article deals with the problem of stochastic stability for a class of discrete-time Markovian jump singular systems. A time-dependent coordinate transformation is provided, under which an equivalent form of the original Markovian jump singular systems can be obtained. This equivalent form not only shows the inherent state jump behavior at the switching instants, but also plays an important role

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This note focuses on the convergence problem of a distributed recursive least squares (RLS) estimator, which converges fast in many circumstances. We find that the convergence behavior of this distributed RLS is quite different for the scalar-parameter and high-dimensional-parameter cases.

We study the convergence properties of an overlapping Schwarz decomposition algorithm for solving nonlinear optimal control problems (OCPs). The algorithm decomposes the time domain into a set of overlapping subdomains, and solves all subproblems defined over subdomains in parallel. The convergence is attained by updating primal-dual information at the boundaries of overlapping subdomains. We show

In this article, we introduce the notion of relative $\mathcal {K}$-equi-stability (RKES) to characterize the uniformly continuous dependence of (weak) solutions on external disturbances for nonlinear parabolic partial differential equations (PDEs). Based on the RKES, we prove the input-to-state stability (ISS) in the spatial sup-norm for a class of nonlinear parabolic PDEs with either Dirichlet or

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

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Requirements on subsystems have been made clear in this article for a linear time invariant networked dynamic system (NDS), under which subsystem interconnections can be estimated from external output measurements. In this NDS, subsystems may have distinctive dynamics, and subsystem interconnections are arbitrary. It is assumed that system matrices of each subsystem depend on its (pseudo) first principle

We propose the ensemble Kalman smoother multiple distribution estimation filter (EnKS-MDEF) for nonlinear state estimation problems. The EnKS-MDEF is an example of the multiple distribution estimation filter (MDEF), which is a particle filter (PF) that estimates the filtered state probability density function (pdf) using multiple conditional state pdfs. The one step behind (OSB) smoothed state pdf

In this article, we present a hierarchical multirate control architecture for nonlinear autonomous systems operating in partially observable environments. Control objectives are expressed using syntactically co-safe linear temporal logic (LTL) specifications and the nonlinear system is subject to state and input constraints. At the highest level of abstraction, we model the system–environment interaction

For most networked systems found in the literature, the actuated boundary is usually located at one end. In this article, we first consider the stabilization of a chain of two interconnected subsystems, actuated at the in-between boundary. Each subsystem corresponds to coupled hyperbolic partial differential equations. Such in-domain actuation leads to higher complexity, and represents a significant

In this article, we propose a new linear differentiator, called extended dynamics differentiator (EDD), by the extended dynamics approach. By a proper choice of extended dynamics, the EDD can make use of the prior signal dynamics as much as possible. As a result, the accuracy of the EDD can be improved greatly provided we have known some signal dynamics before signal differentiation. When all the signal

The consensus control of multiagent systems (MASs) over randomly switching communication topologies has drawn increasing attention from researchers, since the mean square consensus or the most surely consensus is significant and practical. This manuscript focuses on the output consensus problem for heterogeneous MASs with input saturation constraints over the Markovian randomly switching topologies

In this article, we study necessary and sufficient conditions for contraction and incremental stability of dynamical systems with respect to non-Euclidean norms. First, we introduce weak pairings as a framework to study contractivity with respect to arbitrary norms, and characterize their properties. We introduce and study the sign and max pairings for the $\ell _{1}$ and $\ell _\infty$ norms, respectively

We study the problem of synthesizing a controller that maximizes the entropy of a partially observable Markov decision process (POMDP) subject to a constraint on the expected total reward. Such a controller minimizes the predictability of an agent’s trajectories to an outside observer while guaranteeing the completion of a task expressed by a reward function. Focusing on finite-state controllers (FSCs)

We consider a setting where two noncooperative players optimally influence the evolution of an initial spatial probability in a game-theoretic hierarchical fashion (Stackelberg differential game), so that at a specific final time the distribution of the state matches a given final target measure. We provide a sufficient condition for the existence and uniqueness of an optimal transport map and prove

This article is concerned with a compositional approach for the construction of control barrier certificates for large-scale interconnected stochastic systems while synthesizing hybrid controllers against high-level logic properties. Our proposed methodology involves decomposition of interconnected systems into smaller subsystems and leverages the notion of control sub-barrier certificates of subsystems

A reconnaissance penetration game is a classic target-attacker-defender game. In this game, a reconnaissance UAV (namely attacker) tries to avoid the defender and reconnoiter a target as close as possible, whereas a target tries to escape the attacker with the help of defender. Practically, the defender is considered constrained in a certain territory to capture the attacker and help the target. This

Cohesion in networks during transitions from one consensus value to another, i.e., the ability of agents to respond in a similar manner during the transition, can be as important as achieving the new consensus value. Existing decentralized network control strategies mainly concern with the convergence speed to the final consensus value. However, even with increased convergence speed, the level of cohesion

Application of sliding-mode control strategies based on (generalized) super-twisting (ST) algorithms in the presence of time- and state-dependent perturbations is highly challenging. One of the difficulties lies in the occurrence of a kind of algebraic loop; the bounds required for control design require bounds on the control variable, which itself depends on the control to be designed. Existing results

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.

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

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

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

This article considers a codesign problem for industrial networked control systems to ensure both stability and efficiency properties of such systems. This problem is particularly challenging due to the fact that wireless communications in industrial environments are not only subject to shadow fading, but also stochastically correlated with their surrounding environments. This article first introduces

In this article, by using the Brunovsky normal form, we provide a reformulation of the problem consisting in finding the actuator design which minimizes the controllability cost for finite-dimensional linear systems with scalar controls. Such systems may be seen as spatially discretized linear partial differential equations with lumped controls. The change of coordinates induced by Brunovsky’s normal

Robust performance of control schemes for open quantum systems is investigated under classical uncertainties in the generators of the dynamics and nonclassical uncertainties due to decoherence and initial state preparation errors. A formalism is developed to measure performance based on the transmission of a dynamic perturbation or initial state preparation error to the quantum state error. This makes

This article presents a time-invariant extremum seeking controller (ESC) for nonlinear autonomous systems with limit cycles. For this time-invariant ESC, we propose a method to prove the closed-loop system has an asymptotically stable limit cycle. The method is based on a perturbation theorem for maps, and, unlike existing techniques that use averaging and singular perturbation tools, it is not limited

This article adopts a reinforcement learning (RL) method to solve infinite horizon continuous-time stochastic linear quadratic problems, where the drift and diffusion terms in the dynamics may depend on both the state and control. Based on the Bellman’s dynamic programming principle, we presented an online RL algorithm to attain optimal control with partial system information. This algorithm computes

This article studies the tracking control problem of networked multiagent systems under both multiple networks and event-triggered mechanisms. Multiple networks are to connect multiple agents and reference systems with decentralized controllers to guarantee their information transmission, whereas the event-triggered mechanisms are to reduce the information transmission via the networks. In this article

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

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

Communication compression techniques are of growing interests for solving the decentralized optimization problem under limited communication, where the global objective is to minimize the average of local cost functions over a multiagent network using only local computation and peer-to-peer communication. In this article, we propose a novel compressed gradient tracking algorithm (C-GT) that combines

This article presents a novel Jacobi-style iteration algorithm for solving the problem of distributed submodular maximization, in which multiple agents determine their strategies from the private sets so that a global, nonseparable submodular objective function is jointly maximized. Building on the multilinear extension of the submodular function, we expect to achieve the solution from a probabilistic

Attitude estimation is a core problem in many mobile robotic systems, such as unmanned aerial and ground vehicles. The configuration space of these systems is properly modeled by exploiting the theory of Lie groups. In this article, we propose a second-order-optimal minimum-energy filter on the matrix Lie group TSE(2), the tangent bundle of the special Euclidean group SE(2), where the optimality is

Model predictive controllers use dynamics models to solve constrained optimal control problems. However, computational requirements for real-time control have limited their use to systems with low-dimensional models. Nevertheless, high-dimensional models arise in many settings, for example, discretization methods for generating finite-dimensional approximations to partial differential equations can