Finite-time stability involves dynamical systems whose trajectories converge to a Lyapunov stable equilibrium state in finite time. In this paper, we address finite time stability of discrete-time dynamical systems. Specifically, we show that finite time stability leads to uniqueness of solutions in forward time. Furthermore, we provide Lyapunov and converse Lyapunov theorems for finite-time stability

In this paper, we consider a Markov decision process (MDP) in which the ego agent intends to hide its state from detection by an adversary while pursuing a nominal objective. After formulating the detection-averse MDP problem, we first describe a value iteration (VI) approach to exactly solve it. To overcome the “curse of dimensionality” and thus gain scalability to larger-sized problems, we then propose

A generalized Kalman–Bucy model under model uncertainty and a corresponding robust problem are studied in this paper. We find that this robust problem is equivalent to an estimated problem under a sublinear operator. By Girsanov transformation and the minimax theorem, we prove that this problem can be reformulated as a classical Kalman–Bucy filtering problem under a new probability measure. The equation

We derive a constructive sufficient condition for the existence of a compensator such that a prescribed semi-algebraic set is invariant for the resulting closed-loop system. The construction procedure consists of symbolic computations. Although the target system is restricted to polynomial control systems, non-polynomial smooth compensators can be designed. We also derive the procedure for extracting

Many vehicle control systems depend on the body sideslip angle, but robust and cost-effective direct measurement of this angle is yet to be achieved for production vehicles. Estimation from indirect measurements is thus the only viable option. In the paper, a sideslip estimator is obtained through the identification of a linear parameter varying (LPV) model. Although inspired by physical insights into

The objective of the present paper is finite-dimensional observer-based control of the 1-D linear heat equation with constructive and feasible design conditions. We propose a method which is applicable to boundary or non-local sensing together with non-local actuation, or to Dirichlet actuation with non-local sensing. We use a modal decomposition approach. The dimension of the controller, N0, is equal

In this paper, we consider the event-triggered attitude consensus of multiple rigid-body systems. Two event-triggered attitude consensus protocols are designed under the absolute attitude and relative attitude measurement, respectively. For the first case, the gnomonic projection is utilized to project the attitude to the Euclidean plane almost globally. Then, a distributed attitude consensus protocol

In this paper, we study the problem of estimating states and faults for a class of linear time-delay systems using sliding mode observers. Both the states and outputs are subject to constant delays. This is a challenging problem and has not yet been resolved in the literature. By appropriately using a system transformation and the H∞ filtering method, we propose a novel sliding mode observer scheme

This paper considers the problem of simultaneous estimation of the attitude, position and linear velocity for vehicles navigating in a three-dimensional space. We propose two types of hybrid nonlinear observers using continuous angular velocity and linear acceleration measurements as well as intermittent landmark position measurements. The first type relies on a fixed-gain design approach based on

The identification of affinely parameterized state–space system models is quite popular to model practical physical systems or networked systems, and the traditional identification methods require the measurements of both the input and output data. However, in the presence of partial unknown input, the corresponding system identification problem turns out to be challenging and sometimes unidentifiable

In this paper we study robustness properties of discrete-time homogeneous systems. We also analyse stability and robustness properties of a more general class of nonlinear discrete-time systems that can be approximated by homogeneous ones. We apply the results to the investigation of stability properties of discretized continuous-time systems.

This paper introduces a new formulation of dynamic control allocation as a dynamic optimization problem. This optimal control formulation allows us to develop allocation with guaranteed actuator constraints, and to learn the optimal control allocation online using measured data and without knowing the system dynamics. The general solution to this problem is provided in the form of an H∞controller.

This paper focuses on indefinite stochastic mean-field linear–quadratic (MF-LQ, for short) optimal control problems, which allow the weighting matrices for state and control in the cost functional to be indefinite. The solvability of stochastic Hamiltonian system and Riccati equations is presented under indefinite case. The optimal controls in open-loop form and closed-loop form are derived, respectively

New methods are developed for the stabilization of a linear system with general time-varying distributed delays existing at the system’s states, inputs and outputs. In contrast to most existing literature where the function of time-varying delay is continuous and bounded, we assume it to be bounded and measurable. Furthermore, the distributed delay kernels can be any square-integrable function over

In multiagent dynamical systems, privacy protection corresponds to avoid disclosing the initial states of the agents while accomplishing a distributed task. The system-theoretic framework described in this paper for this scope, denoted dynamical privacy, relies on introducing output maps which act as masks, rendering the internal states of an agent indiscernible by the other agents. Our output masks

An aggregative game involving double-integrator agents is investigated. In this game, the dynamics of all players are subjected to unknown time-varying disturbances and unmodeled terms, and are also influenced by networked attacks on the communication topology. To seek a Nash equilibrium for such games, a novel distributed robust Nash equilibrium seeking algorithm is proposed and the complete closed-loop

In Marconi et al. (2007), the theory of nonlinear Luenberger observers was exploited to prove that a solution to the asymptotic output regulation problem for minimum-phase normal forms always exists. The paper provided an existence result and a very general regulator structure, although unfortunately, no constructive method was given to design all the degrees of freedom of the regulator. In this paper

This paper addresses the tracking control problem of a class of high-order uncertain nonlinear systems under time-varying asymmetric output constraints. Most relevant results in the literature have two main restrictions: R1) some constraints need to be imposed on powers and growth conditions have to be established for the nonlinear functions of the system; R2) nonlinear bounding functions must be derived

This paper addresses the problem of finding optimal output feedback strategies for solving linear differential zero-sum games using a model-free approach based on adaptive dynamic programming (ADP). In contrast to their discrete-time counterparts, differential games involve continuous-time dynamics and existing ADP approaches to their solutions require access to full measurement of the internal state

Multiple integrator systems with input saturation and state constraints ubiquitously exist in practical problems such as trajectory planning in CNC (computer numerical control) systems, robots, automotive systems and industrial processes. Without state constraints, the optimal control of the multiple integrator with only input saturation is well solved in classic optimal control theory. However, if

This paper studies the cooperative optimal control for multi-agent systems (MASs) with Lipschitz nonlinearities over general digraphs. The leader-following consensus model consisting of multiple followers and one leader is constructed. Distributed optimal control protocols using the linear quadratic regulator approach are designed. Under the proposed protocols, the performance index of the MAS is optimized

A mathematical framework to predict the Unscented Kalman Filter (UKF) performance improvement relative to the Extended Kalman Filter (EKF) using a quantitative measure of non-linearity is presented. It is also shown that the range of performance improvement the UKF can attain, for a given minimum probability depends on the Non-linearity Indices of the corresponding system and measurement models. Three

With the proliferation of distributed energy resources (DERs), voltage regulation in active distribution networks (ADNs) has been facing a great challenge. This paper derives an asynchronous distributed voltage control strategy based on the partial primal–dual gradient algorithm, where both active and reactive power of DERs are considered. Different types of asynchrony due to imperfect communication

Driven by the increasing needs in the process industry for designing fault-tolerant control systems based on process data and maintaining its performance during online operation, data-driven realization and design of feed-forward fault-tolerant control systems with embedded residual generation are studied. To this end, a parameterized and data-driven realization form of stable image representation

Linear proportional ISS synthesis of parabolic systems is developed within the practical framework of in-domain embedded sensing and actuation. The underlying system is affected by external disturbances and it is governed by a non-homogeneous reaction–diffusion PDE with a priori unknown spatially varying parameters. The present investigation focuses on practically motivated sampled-in-space sensing

This paper studies observer-based output feedback consensus control of networked homogeneous systems in the presence of unknown bounded actuator and sensor delays. A transport partial differential equation (PDE) is used to describe the dynamics of the delay state, and then a distributed observer on the basis of the estimate delay state and relative output information is designed to estimate the neighborhood

This work aims to achieve output consensus among heterogeneous agents in a multi-agent environment where each agent is subject to state and/or control constraints. The communication among agents is described by a directed graph that switches with time. Past works in this direction are much fewer than the constraint-free case and most results are restricted to the case where the agents are homogeneous

Suitable continuity and boundedness assumptions on the function f defining the dynamics of a time-varying nonimpulsive system with inputs are known to make the system inherit stability properties from the zero-input system. Whether this type of robustness holds or not for impulsive systems was still an open question. By means of suitable (counter)examples, we show that such stability robustness with

Although the fundamental problem of asymptotic tracking and disturbance rejection in control theory has been well studied, the independence of convergence rate of the tracking error on structures of feedforward controllers has been overlooked. In such control design, many feedforward controllers can be constructed and it is of practical importance to know whether all feedforward controllers actually

This paper presents two distributed event-triggered algorithms under directed communication networks to solve a class of convex optimization problems such as the economic dispatch problem (EDP) with equality constraint, while the objective of optimization is the sum of all locally convex functions. One is distributed continuous-time event-triggered optimization algorithm, and the other is discrete-time

In this contribution we show that under some circumstances the Kalman–Yakubovich–Popov (KYP) lemma can be applied for testing quadratic stability of multi-mode switched linear systems. Based on this observation, we introduce several constructive algorithms which enable us to associate a transfer function matrix to a switched linear system given in general form. The strict positive realness test of

This paper addresses the problem of determining the response peak of dynamical systems, a classical problem in control systems. The paper starts by considering the impulse response of linear time-invariant (LTI) systems. A linear matrix inequality (LMI) condition for establishing upper bounds of the sought peak is proposed by embedding the trajectory onto the level set of a polynomial and by introducing

An event-triggered robust state estimation problem for linear time-varying systems subject to Gaussian noises and non-stochastic unknown exogenous inputs is investigated in this work. To design the estimator, the state estimation problem is formulated as an optimization problem with a risk-sensitive cost function. This problem is solved by constructing a reference probability measure, under which the

We propose and analyze a real-time model predictive control (MPC) scheme that utilizes stored data to improve its performance by learning the value function online with stability guarantees. For linear and nonlinear systems, a learning method is presented that makes use of basic analytic properties of the cost function and is proven to learn the MPC control law and the value function on the limit set

This study investigates the leader-following consensus problem for heterogeneous multi-agent systems subject to both sensor and actuator attacks. The attacks considered in this paper are false data injection attacks. A novel adaptive controller is proposed to guarantee that the consensus tracking is achieved with cooperative uniform ultimate boundedness for the multi-agent systems in the simultaneous

Integral action is an essential component for offset-free response in many feedback control systems. Standard internal model control design rules ensure an offset-free response for open-loop stable plants. In this paper a linear feedback control structure is proposed that comprises an observer using an augmented plant model, state estimate feedback and disturbance estimate feedback. This allows internal

In this paper, the finite-time leader-following output consensus problem is investigated for a multi-agent system subjected to directed topology and disturbance. Firstly, a distributed finite-time extended state observer (DFTESO) is designed to provide estimate for unmeasured consensus errors and disturbances. The sufficient condition is provided in terms of linear matrix inequality (LMI) to ensure

Strong Lyapunov functions for two classical problems in adaptive control and parameter identification are presented. These Lyapunov functions incorporate in their structure the classical persistency of excitation conditions, allowing to show global uniform asymptotic stability of the associated adaptive systems under sufficient and necessary conditions.

We describe a consensus-based distributed filtering algorithm for linear systems with a parametrized gain and show that when the parameter becomes large the error covariance at each node becomes arbitrarily close to the error covariance of the optimal centralized Kalman filter. The result concerns distributed estimation over a connected un-directed or directed graph and for static configurations it

In this paper, we propose an inexact Augmented Lagrangian Method (ALM) for the optimization of convex and nonsmooth objective functions subject to linear equality constraints and box constraints where errors are due to fixed-point data. To prevent data overflow we also introduce a projection operation in the multiplier update. We analyze theoretically the proposed algorithm and provide convergence

Recent years have seen several new directions in the design of sparse control of cyber–physical systems (CPSs) driven by the objective of reducing communication costs. One common assumption made in these designs is that the communication happens over a dedicated network. For many practical applications, however, communication must occur over shared networks, leading to two critical design challenges

Techniques known as Nonlinear Set Membership prediction or Lipschitz Interpolation are approaches to supervised machine learning that utilise presupposed Lipschitz properties to perform inference over unobserved function values. Provided a bound on the true best Lipschitz constant of the target function is known a priori, they offer convergence guarantees, as well as bounds around the predictions.

A method is presented to estimate the region of attraction (ROA) of stochastic systems with finite second moment and uncertainty-dependent equilibria. The approach employs Polynomial Chaos (PC) expansions to represent the stochastic system by a higher-dimensional set of deterministic equations. We first show how the equilibrium point of the deterministic formulation provides the stochastic moments

A classical result in spectral estimation establishes that the relative entropy rate between two zero-mean stationary Gaussian processes can be computed explicitly in terms of their spectral densities, hence inducing a pseudo-distance in the cone of positive definite spectra. Relying on the properties of multi-level circulant and multi-level Toeplitz matrices, we establish a similar theory for homogeneous

A technique of linearizing what we call expectation-based inequality conditions is proposed for control of discrete-time linear systems with stochastic dynamics. In particular, the coefficient random matrices of the systems are assumed to be represented with random polytopes, and the linearization technique is discussed so as to appropriately deal with associated uncertainties. Our expectation-based

This paper introduces a framework for analyzing a general class of uncertain nonlinear discrete-time systems with given state-, control-, and disturbance constraints. In particular, we propose a set-theoretic generalization of the concept of dissipativity for systems that are affected by external disturbances. The corresponding theoretical developments build upon set based analysis methods and lay

Recently, Romdlony and Jayawardhana (2016) proposed control Lyapunov–Barrier functions (CLBFs) for the stabilization of nonlinear control systems while avoiding a bounded set of unsafe states. We demonstrate that CLBFs used in Romdlony and Jayawardhana (2016, Prop. 3 and 5) cannot exist. Critically, this implies that the examples discussed in Romdlony and Jayawardhana (2016) do not satisfy the stated

Globalized dual heuristic programming (GDHP) algorithm is a special form of approximate dynamic programming (ADP) method that solves the Hamilton–Jacobi–Bellman (HJB) equation for the case where the system takes control-affine form subject to the quadratic cost function. This study incorporates the deep neural networks (DNNs) as a function approximator to inherit the advantages of which to express

For time-invariant (nonimpulsive) systems, it is already well-known that the input-to-state stability (ISS) property is strictly stronger than integral input-to-state stability (iISS). Very recently, we have shown that under suitable uniform boundedness and continuity assumptions on the function defining system dynamics, ISS implies iISS also for time-varying systems. In this paper, we show that this

Priority-based scheduling strategies are often used to resolve contentions in resource constrained control systems. Such scheduling strategies inevitably introduce time delays into controls and may degrade the performance of control systems. Considering the coupling between priority assignment and control, this paper presents a method to co-design priority assignments and control laws for each control

This paper investigates the stabilization problem for switched linear systems with all modes unstable via designing switching laws. By introducing an associated system whose stability ensures that the original switched system is stable, novel sufficient conditions for the stability of switched systems are proposed. Based on the obtained stability conditions, an effective periodical switching law design

It is innovatively established, through a nonlinear Persistency of Excitation (PE) analysis, that the latest Bernard–Praly gradient adaptive observer – for nonsalient-pole surface Permanent Magnet Synchronous Motors (PMSMs) with uncertain flux of the permanent magnet (PM) – owns exponential convergence properties under well-known observability conditions. Such exponential properties can be crucially

We study time-varying linear discrete time systems with uncertainties and time-varying measurement delays, whose outputs are perturbed by uncertainty. We build sequential predictors, which ensure input-to-state stability with respect to the uncertainties and which can be constructed using output values under arbitrarily long delays. The number of required sequential predictors is any upper bound for

This study considers the problem of periodic event-triggered (PET) cooperative output regulation for a class of linear multi-agent systems. The advantage of the PET output regulation is that the data transmission and triggered condition are only needed to be monitored at discrete sampling instants. It is assumed that only a small number of agents can have access to the system matrix and states of the

This paper investigates the disturbance decoupling problem by dynamic output feedback in the general case of systems with possible input–output feedthrough matrices. In particular, we aim to extend the geometric condition based on self-boundedness and self-hiddenness, which enables to solve the decoupling problem without requiring eigenspace computations. We show that, exactly as in the case of zero

This paper studies finite-time stability analysis and finite-time stabilization of linear systems by bounded linear time-varying feedback. On the one hand, (both local and global) finite-time stability of general nonlinear time-varying systems is investigated by the comparison principle and the notion of finite-time escaping functions. Some Lyapunov-like stability theorems are established. On the other

We investigate the benefit of operating the chemostat model with periodic controls for biological water decontamination. The first problem that we consider is to minimize the average output concentration of pollution under a constraint on the total quantity of water treated over the period. The second one consists in maximizing this quantity under a constraint on the average output concentration. We

In a recent article Pal et al. (2020), an arbitrary time convergence controller design method is proposed for a nth order nonlinear system (n≥1). Although the analysis of the Lyapunov characterization for free-will arbitrary time stable systems (Pal et al. (2020)[Thm. 1]) and the controller design for first order system are correct, the validity of the further extensions to second and higher-order

In this paper, the stability problem of a class of planar nonlinear systems is investigated. Motivated by the Routh–Hurwitz stability criterion for planar linear systems, a necessary and sufficient condition for stability of a class of planar nonlinear systems is established. To prove the necessity, a new method called particular solution method is provided to justify instability. In addition, a sufficient

This paper investigates the long input delay problem in consensus control of multi-agent systems with directed graph. First, cascade structure predictive observers are designed to obtain the future state for each agent. Then, adaptive technique based consensus controllers are designed for the agents to make sure that any global information is not needed. Lyapunov–Krasovskii functionals are used for