Control For Uncertain Stochastic Systems Research Articles

Understanding the Capability of PD Control for Uncertain Stochastic Systems

In this article, we focus on the global stabilizability problem for a class of uncertain stochastic control systems, where both the drift term and the diffusion term are nonlinear functions of the state variables and the control variables. We will show that the widely applied proportional-derivative (PD) control in engineering practice has the ability to globally stabilize such systems in the mean square sense, provided that the upper bounds of partial derivatives of the nonlinear functions satisfy a certain algebraic inequality. It will also be proved that the stabilizing PD parameters can only be selected from a two dimensional bounded convex set, which differs significantly from the existing results for PD controlled stochastic systems where the diffusion term does not depend on the control variables. Moreover, a particular polynomial on these bounds is introduced, which can be used to determine under what conditions the system is not stabilizable by the PD control, and thus demonstrating the fundamental limitations of PD control.

Guaranteed cost fault-tolerant control for uncertain stochastic systems via dynamic event-triggered adaptive dynamic programming

It is difficult to apply the event-triggered adaptive dynamic programming (ET-ADP) algorithm to Itô-type stochastic systems due to stochastic disturbances. Therefore, few studies have addressed the ET-ADP algorithm for Itô-type stochastic systems. To fill this gap, this paper investigates a guaranteed cost fault-tolerant control problem for uncertain stochastic systems via a dynamic ET-ADP algorithm. First, the original control problem is transformed into the optimal control problem of a nominal system, and sufficient criteria are presented to verify the feasibility of the problem transformation. Second, a dynamic event-triggered condition is designed. Then, the optimal control of the nominal system is achieved via an ET-ADP algorithm. Finally, a numerical simulation and a comparative experiment are presented to illustrate the effectiveness of the developed control scheme.

Event-triggered control for uncertain stochastic systems under triple network attacks

This paper studies the control problem of uncertain stochastic systems, which takes into account the impact of network attacks. The types of network attacks considered are denial-of-service (DoS) attacks, deception attacks and replay attacks. In order to save network resources and improve communication utilization, the static event-triggered mechanism and adaptive event-triggered mechanism are cited respectively. Firstly, a new Lyapunov-Krasovskii functional is constructed, employing improved Wirtinger-based integral inequality and Jensens inequality, the criteria on stochastic stability in the mean square for uncertain stochastic systems are proposed. Secondly, the design methods of static event-triggered controller and adaptive event-triggered controller are given respectively. Finally, a practical example is given to manifest the effectiveness of the theoretical results.

Non‐fragile robust exponential stabilisation and control for uncertain stochastic systems with non‐linearity and mixed delays

This study focuses on the delay-dependent robust exponential stabilisation and H ∞ control for uncertain stochastic time-delay systems with non-linear terms. Uncertain parameters are assumed to be time-varying norm bounded, while time-varying delay terms include both discrete and distributed delays. Firstly, by choosing an appropriate Lyapunov–Krasovskii functional, a sufficient condition for the robust exponential stabilisation is obtained. Secondly, the H ∞ control is also discussed. All criteria are presented in the form of linear matrix inequalities with less conservatism. Finally, an example verifies the validity of the proposed method.

Robust H∞-Control for Uncertain Stochastic Systems with Impulsive Effects

Robust stabilization and H ∞ controller design for uncertain systems with impulsive and stochastic effects have been deeply discussed. Some sufficient conditions for the considered system to be robustly stable are derived in terms of linear matrix inequalities (LMIs). In addition, an example with simulations is given to better demonstrate the usefulness of the proposed H ∞ controller design method.

A Parameter-Dependent Sliding Mode Approach for Finite-Time Bounded Control of Uncertain Stochastic Systems With Randomly Varying Actuator Faults and Its Application to a Parallel Active Suspension System

This paper addresses the mean-square finite-time bounded control problem for uncertain stochastic systems via a sliding mode approach. The stochastic phenomena of randomly occurring uncertainties and randomly varying actuator faults modeled by two independent exponential distributions are addressed effectively. A key issue for the system under the consideration is how to ensure, for any prescribed finite (possibly short ) working time interval, the stochastic finite-time boundedness (SFTB) of the resultant closed-loop systems and the reachability of the specified sliding surface in mean-square sense. To this end, a parameter-dependent sliding mode control (SMC) law is designed to force ( with probability one ) the state trajectories into a domain around the specified sliding surface during the given finite-time interval. The upper bound of the sliding domain associated with the design parameters is obtained explicitly. The sufficient conditions are established, respectively, for guaranteeing the SFTB of the SMC systems over both reaching phase and sliding motion phase . Finally, the proposed finite-time SMC approach is illustrated via a parallel active suspension system.

Robust H∞ Control of Uncertain Stochastic Systems with Time-varying Interval Delays

A robust delay-dependent stability criterion for discrete-time uncertain stochastic systems is proposed to achieve asymptotical stability and H∞ performance in this paper. Based on modeling approaches, Linear Parameter Varying (LPV) system with multiplicative noise term is built to represent uncertain stochastic systems. Moreover, state and input delays are considered as two individual time-varying interval cases for general effect. Employing a novel Lyapunov-Krasovskii function, Jensen inequality and transform technology, some relaxed sufficient conditions are derived into Linear Matrix Inequality (LMI) forms to apply convex optimization algorithm. Through solving the derived conditions, Gain-Scheduled (GS) controller can be designed such that robust asymptotical stability and H∞ performance of closed-loop system are achieved in the mean square. At last, two numerical examples are provided to demonstrate applicability and effectiveness of this paper.

Observer-based state tracking control of uncertain stochastic systems via repetitive controller

ABSTRACTThis paper develops the repetitive control scheme for state tracking control of uncertain stochastic time-varying delay systems via equivalent-input-disturbance approach. The main purpose of this work is to design a repetitive controller to guarantee the tracking performance under the effects of unknown disturbances with bounded frequency and parameter variations. Specifically, a new set of linear matrix inequality (LMI)-based conditions is derived based on the suitable Lyapunov–Krasovskii functional theory for designing a repetitive controller which guarantees stability and desired tracking performance. More precisely, an equivalent-input-disturbance estimator is incorporated into the control design to reduce the effect of the external disturbances. Simulation results are provided to demonstrate the desired control system stability and their tracking performance. A practical stream water quality preserving system is also provided to show the effectiveness and advantage of the proposed approach.

Robust stabilization andH∞control of uncertain stochastic time-delay systems with nonlinear perturbation

Summary This paper investigates the problem of delay-dependent robust stochastic stabilization and H∞ control for uncertain stochastic nonlinear systems with time-varying delay. System uncertainties are assumed to be norm bounded. Firstly, by using novel method to deal with the integral terms, robustly stochastic stabilization results are obtained for stochastic uncertain systems with nonlinear perturbation, and an appropriate memoryless state feedback controller can be chosen. Compared with previous results, the new technique can sufficiently utilize more negative items information. Then, robust H∞ control for uncertain stochastic system with time-varying delay and nonlinear perturbation is considered, and the controller is designed, which will guarantee that closed-loop system is robustly stochastically stable with disturbance attenuation level. Finally, two numerical examples are listed to illustrate that our results are effective and less conservative than other reports in previous literature. Copyright © 2016 John Wiley & Sons, Ltd.

Formula omitted] tracking of uncertain stochastic time-delay systems: Memory state-feedback controller design

The problem of state robust H∞ tracking control for uncertain stochastic systems with interval time-varying delay is considered in this paper. The target is to design a memory state feedback controller such that the resulting closed-loop augmented system is robustly stochastically asymptotically stable and the states of original systems can follow the reference signal with given H∞ performance. Firstly, by constructing delay-partitioning-dependent Lyapunov–Krasovskii functional with reciprocally convex approach, a delay-dependent condition guaranteeing the robust H∞ tracking performance is proposed in a set of matrix inequalities. Secondly, new stability criteria for stochastic systems with time-varying delay are given with less conservativeness than some recent results. Thirdly, memory state feedback controller is designed via a set of linear matrix inequalities (LMIs) which can be solved by Matlab LMI toolbox. At last, numerical simulations are addressed to show the effectiveness of the proposed methods.

A novel adaptive switching function on fault tolerable sliding mode control for uncertain stochastic systems

A novel switching function based on an optimization strategy for the sliding mode control (SMC) method has been provided for uncertain stochastic systems subject to actuator degradation such that the closed-loop system is globally asymptotically stable with probability one.In the previous researches the focus on sliding surface has been on proportional or proportional-integral function of states. In this research, from a degree of freedom that depends on designer choice is used to meet certain objectives.In the design of the switching function, there is a parameter which the designer can regulate for specified objectives. A sliding-mode controller is synthesized to ensure the reachability of the specified switching surface, despite actuator degradation and uncertainties. Finally, the simulation results demonstrate the effectiveness of the proposed method.

Delay-dependent robust H∞ control for uncertain stochastic systems with time-varying delays in state and control input

This article deals with the robust H∞ control problem for uncertain stochastic systems with time-varying delays in state and control input. The time delay is assumed to be a time-varying continuous function varying in an interval and uncertainties are assumed to be norm bounded. New delay-dependent criteria for the existence of memoryless state feedback H∞ controller are proposed to guarantee robust asymptotic stability in the mean square as well as the prescribed H∞ performance level of the closed-loop systems for all admissible uncertainties. The main contribution of this article is the instrumental idea of delay decomposing, which leads the resultant conditions to be much less conservative than the existing results in the literature with the decomposing getting thinner. By using free-weighting matrices and a new technique to estimate the upper bound of the stochastic differential of Lyapunov–Krasovskii functional candidate, new delay-dependent conditions are derived by considering the relationship among the time-varying delay and its lower and upper bounds without ignoring any useful terms. The advantage of the results proposed in this article lies in their reduced conservatism, as shown via illustrative examples, which also demonstrates the effectiveness of the proposed method.

Robust reliable sampled‐data H∞ control for uncertain stochastic systems with random delay

In this article, the problem of robust reliable sampled‐data control for a class of uncertain nonlinear stochastic system with random delay control input against actuator failures has been studied. In the considered system, the parameter uncertainty satisfies the norm bounded condition and the involved time delay in control input are assumed to be randomly time‐varying which is modeled by introducing Bernoulli distributed sequences. By constructing a novel Lyapunov–Krasovskii functional involving with the lower and upper bounds of the delay, a new set of sufficient conditions are derived in terms of linear matrix inequalities (LMIs) for ensuring the robust asymptotic stability of the uncertain nonlinear stochastic system with random delay and disturbance attenuation level about its equilibrium point for all possible actuator failures. In particular, Schur complement together with Jenson's integral inequality is utilized to substantially simplify the derivation in the main results. The derived analytic results are applied to design robust reliable sampled‐data controller for hanging crane structure model and simulation results are provided to demonstrate the effectiveness of the proposed control law. © 2014 Wiley Periodicals, Inc. Complexity 21: 42–58, 2015

Optimal Control of Uncertain Stochastic Systems with Markovian Switching and Its Applications to Portfolio Decisions

This article first describes a class of uncertain stochastic control systems with Markovian switching, and derives an Itô-Liu formula for Markov-modulated processes. We characterize an optimal control law, that satisfies the generalized Hamilton-Jacobi-Bellman (HJB) equation with Markovian switching. Then, by using the generalized HJB equation, we deduce the optimal consumption and portfolio policies under uncertain stochastic financial markets with Markovian switching. Finally, for constant relative risk-aversion (CRRA) felicity functions, we explicitly obtain the optimal consumption and portfolio policies. Moreover, we make an economic analysis through numerical examples.

Network-based H∞ output feedback control for uncertain stochastic systems

This paper investigates the problem of network-based H∞ output feedback control for a class of stochastic nonlinear systems. A novel model is proposed to describe the systems taken into two sides of communication channels in the network environment, which is more general than one side of communication channel. The design procedure of observer-based controller is presented, which guarantees the asymptotic stability in the mean square of the resulting closed-loop system with an H∞ performance. Finally, a crane example is utilized to show the effectiveness and potential of the developed techniques.

On design of robust reliable [formula omitted] control and input-to-state stabilization of uncertain stochastic systems with state delay

This paper is concerned with the problem of designing a robust reliable H∞ control for uncertain stochastic systems with time delay (USSD) and time-varying norm-bounded parametric uncertainties in the system states. The faulty actuators are considered as a disturbance signal to the system which is augmented with system disturbance input. The main objective of the paper is presenting a state feedback controller that guarantees input-to-state stability (ISS) of the plant and an H∞ norm-bound constraint on the attenuation of the augmented disturbance for all admissible uncertainties and actuator failures. The problem is solved by using Lyapunov functions together with the Razumikhin methodology. To clarify the proposed results, some illustrative examples are presented.

Reliable control of stochastic systems via sliding mode technique

SUMMARYThis paper considers the problem of sliding mode control for uncertain stochastic systems with possible occurrence of actuator faults. There exist parameter uncertainties and state‐dependent noise. Moreover, the faults may happen in any of the actuators. The reliable designing on both passive and adaptive sliding mode controllers is investigated, respectively. Both the reachability of the specified sliding surface and the stochastic stability of the sliding motion are analyzed using the stochastic Lyapunov theory. Finally, numerical simulation results are given.Copyright © 2012 John Wiley & Sons, Ltd.

DELAY-DEPENDENT ROBUST STABILIZATION AND H&#8734 CONTROL FOR UNCERTAIN STOCHASTIC T-S FUZZY SYSTEMS WITH MULTIPLE TIME DELAYS

In this paper, the problems of robust stabilization and H1 control for uncertain stochastic systems with multiple time delays represented by the Takagi-Sugeno (T-S) fuzzy model have been studied. By constructing a new Lyapunov-Krasovskii functional (LKF) and using the bounding techniques, sufficient conditions for the delay-dependent robust stabilization and H1 con- trol scheme are presented in terms of linear matrix inequalities (LMIs). By solving these LMIs, a desired fuzzy controller can be obtained which can be easily calculated by Matlab LMI control toolbox. Finally, a numerical simula- tion is given to illustrate the effectiveness of the proposed method.

Robust [formula omitted] control for stochastic systems with nonlinearity, uncertainty and time-varying delay

This paper deals with the problems of robust stochastic stabilization and H∞ control for uncertain stochastic systems with time-varying delay and nonlinear perturbation. System uncertainties are assumed to be norm bounded and time delay is assumed to be bound and time varying with delay-derivative bounded by a constant, which may be greater than one. First, new delay-dependent criterion is proposed by exploiting delay-partitioned Lyapunov–krasovskii functional and by employing tighter integral equalities to estimate the upper bound of the stochastic differential of Lyapunov–krasovskii functional without ignoring some useful terms. Second, based on the criterion obtained, a delay-dependent criterion for the existence of a state feedback H∞ controller that ensures robust stochastic stability and a prescribed H∞ performance level of the closed-loop system for all admissible uncertainties is proposed. These developed results have advantages over some previous ones, in that they involve fewer matrix variables but have less conservatism and they also enlarge the application scope. New sufficient conditions are presented in terms of linear matrix inequality. Numerical examples are used to illustrate the effectiveness and feasibility of the proposed method.

Delay-dependent non-fragile robust stabilization and H∞ control of uncertain stochastic systems with time-varying delay and nonlinearity

This paper deals with the problems of non-fragile robust stochastic stabilization and robust H ∞ control for uncertain stochastic nonlinear time-delay systems. The parameter uncertainties are assumed to be time-varying norm-bounded appearing in both state and input matrices. The time-delay is unknown and time-varying with known bounds. The non-fragile robust stochastic stabilization problem is to design a memoryless non-fragile state feedback controller such that the closed-loop system is robustly stochastically stable for all admissible parameter uncertainties. The purpose of robust H ∞ control problem, in addition to robust stochastical stability requirement, is to reduce the effect of the disturbance input on the controlled output to a prescribed level. Using the Lyapunov functional method and free-weighting matrices, delay-dependent sufficient conditions for the solvability of these problems are established in terms of linear matrix inequality (LMI). Numerical example is provided to show the effectiveness of the proposed theoretical results.