Stochastic Singular Systems Research Articles

Exponential stability and interval stability of a class of stochastic hybrid systems driven by both Brownian motion and Poisson jumps

A class of stochastic singular hybrid systems driven by both Brownian motion and Poisson jumps are studied. This paper is devoted to discussing the exponential stability and interval stability of such stochastic singular hybrid systems. The concept of interval admissibility is proposed. Sufficient conditions are given for exponential mean square admissibility and interval admissibility by using Itô’s formula, H-representation and spectrum technique. Finally, two simulation cases are presented to demonstrate the theoretical results.

Asymptotic stability in probability of singular stochastic systems with Markovian switchings

SummaryThis paper investigates the problem of asymptotic stability in probability for singular stochastic systems with Markovian switchings. A stochastic Lyapunov theorem on asymptotic stability in probability for the considered systems is provided. Also, we show that the original system has the same stability property as its difference‐algebraic form based on singular value decomposition. By utilizing the earlier results, a sufficient condition is obtained in terms of linear matrix inequalities, which is easy to check by using standard software. Copyright © 2017 John Wiley & Sons, Ltd.

Fault Detection and Diagnosis for Non-Gaussian Singular Stochastic Distribution Systems via Output PDFs

This paper investigates the problem of fault detection and diagnosis (FDD) problem for non-gausian singulat stochastic distribution control (SDC) systems via the output probability density functions(PDFs). The PDFs can be approximated by using square-root B-spline expansion,via this expansions to represent the dynamics weighting systems between the system input and the weights related to the output PDFs. In this works ,an optimal fault detection and diagnosis algorith is present by introducing the parameter-updating .when the fault occurs, an adaptive network parameter-updating law is designed to approximated the fault. Finally, the simulation result are given to show that the approach can detect faults and estimate the size of fault.

Observer‐based adaptive control of uncertain stochastic singular systems via integral sliding mode technique

This study is concerned with the problem of adaptive sliding mode control (SMC) for uncertain stochastic singular systems. A novel integral-type sliding surface function is first introduced based on a particular observer design, which incorporates both the state estimations and the outputs to achieve prescribed specifications. The analysis of mean-square asymptotic admissibility of the underlying sliding mode dynamics with H ∞ disturbance attenuation level for the closed-loop systems is performed to exploit a new condition via linear matrix inequality technique. Then, the reachability of the predesigned sliding surface is ensured within finite-time almost surely by utilising a novel adaptive SMC law. Two examples are provided to demonstrate the validity and potential of the proposed method.

Mean square exponential stability of uncertain singular stochastic systems with discrete and distributed delays

The problems of exponential stability for a class of the uncertain singular stochastic systems with discrete and distributed delays are studied. By using a Lyapunov–Krasovskii functional approach and terms of linear matrix inequalities (LMIs) and the Leibniz–Newton formula, mean square exponential stability criteria ensuring robust stability of the uncertain singular stochastic systems with discrete and distributed delays are established. New mean square exponential stable criteria for the certain singular stochastic systems with discrete and distributed delays are obtained as well. Finally, the validity of the obtained results is shown by a numerical example.

Stability of polytopic-type uncertain singular stochastic systems

The problems of robust stability for a class of the polytopic-type uncertain singular stochastic systems with time-varying delays are studied. By using a delay decomposition approach and terms of linear matrix inequalities (LMIs), robust stability criteria ensuring globally stochastically asymptotic stability of the polytopic-type uncertain singular stochastic systems with time-varying delays are established. New globally stochastically asymptotic stable criteria for the certain stochastic systems with discrete and distributed delays are obtained in terms of linear matrix inequalities and Leibniz–Newton formula as well. Finally, the validity of the obtained results is shown by a numerical example.

Fault tolerant control for a class of nonlinear non-Gaussian singular stochastic distribution systems

New fault diagnosis and active fault tolerant control (FTC) algorithms are proposed for a class of nonlinear singular stochastic distribution control (SDC) systems in this paper. Different from general SDC systems, in singular SDC systems, the relationship between the weights and the control input is expressed by a singular state space model, which increases the difficulty in design of fault diagnosis and fault tolerant control. A non-singular state transformation is made to transform the singular dynamic system into a differential-algebraic system. An adaptive nonlinear observer is designed to estimate the size of the fault occurring in the system. Furthermore, the linear matrix inequality (LMI) approach is applied to establish sufficient conditions for the existence of the observer. Based on the estimated fault information, the active fault tolerant controller is designed to make the post-fault probability density function (PDF) still track the given distribution. At last, an illustrated example is given to demonstrate the effectiveness of the proposed algorithm, and satisfactory results have been obtained.

Fault tolerant control for a class of nonlinear non-Gaussian singular stochastic distribution systems

New fault diagnosis and active fault tolerant control (FTC) algorithms are proposed for a class of nonlinear singular stochastic distribution control (SDC) systems in this paper. Different from general SDC systems, in singular SDC systems, the relationship between the weights and the control input is expressed by a singular state space model, which increases the difficulty in design of fault diagnosis and fault tolerant control. A non-singular state transformation is made to transform the singular dynamic system into a differential-algebraic system. An adaptive nonlinear observer is designed to estimate the size of the fault occurring in the system. Furthermore, the linear matrix inequality (LMI) approach is applied to establish sufficient conditions for the existence of the observer. Based on the estimated fault information, the active fault tolerant controller is designed to make the post-fault probability density function (PDF) still track the given distribution. At last, an illustrated example is given to demonstrate the effectiveness of the proposed algorithm, and satisfactory results have been obtained.

Linear quadratic Pareto optimal control problem of stochastic singular systems

This paper is concerned with the finite horizon linear quadratic (LQ) Pareto optimal control problem of stochastic singular systems. By means of the square completion technique, for the finite horizon LQ optimal control of stochastic singular systems, we establish a new kind of generalized differential Riccati equations (GDREs) and present the existence condition of the solution of the GDREs. Then, for the finite horizon LQ Pareto optimal control, it is shown that under the solvability of the corresponding GDREs, all Pareto candidates can be obtained by solving a weighting sum optimal control. Finally, an example is provided to show the effectiveness of our main results.

Finite‐time stability of fractional‐order stochastic singular systems with time delay and white noise

In this article, the finite‐time stochastic stability of fractional‐order singular systems with time delay and white noise is investigated. First the existence and uniqueness of solution for the considered system is derived using the basic fractional calculus theory. Then based on the Gronwall's approach and stochastic analysis technique, the sufficient condition for the finite‐time stability criterion is developed. Finally, a numerical example is presented to verify the obtained theory. © 2016 Wiley Periodicals, Inc. Complexity 21: 370–379, 2016

Minimum entropy fault‐tolerant control for non‐Gaussian singular stochastic distribution systems

This study presents a new fault diagnosis (FD) and fault-tolerant control (FTC) algorithm for a discrete-time non-Gaussian singular stochastic distribution control (SDC) system. An adaptive observer is used to diagnose the fault of the singular stochastic distribution system. Furthermore, the gain of the observer and adaptive updated law can be formulated by solving the corresponding linear matrix inequality. Based on the estimated fault information, the controller is reconfigured by minimising the performance index with regard to the entropy subjected to mean constraint. The reconfigured controller can make the output of the post-fault SDC system still have the minimum uncertainty, leading to the minimum entropy FTC of the non-Gaussian singular SDC system. Computer simulations are given to demonstrate the validity of the FD and minimum entropy FTC algorithms.

Stability and exact observability of discrete stochastic singular systems based on generalised Lyapunov equations

The stability and exact observability problems of discrete stochastic singular systems based on generalised Lyapunov equations are investigated in this study. First, some new conditions for the existence and uniqueness of the solutions to discrete stochastic singular systems are given, and then, a new type generalised Lyapunov equation is proposed. Based on these results, a sufficient condition for stochastic stability of the systems is derived via the solution of the proposed generalised Lyapunov equation. Moreover, the relationship between the solution of the generalised Lyapunov equation and structure properties of discrete stochastic singular systems is discussed as well. Especially, the relationship between the solution of the generalised Lyapunov equation and the stochastic stability of discrete stochastic singular systems with non-causal behaviour is studied for the first time. Second, another new type generalised Lyapunov equation for exactly observable discrete stochastic singular systems is proposed. Meanwhile, the relationships among the stochastic stability of the systems, exact observability and the solution of the proposed generalised Lyapunov equation are investigated. Finally, simulation examples are worked out to validate the effectiveness of the obtained theoretical results.

Fault diagnosis and fault tolerant control for non-Gaussian time-delayed singular stochastic distribution systems

Stochastic distribution control (SDC) is a new branch of stochastic system control that the system output is the probability density function (PDF) of the output. In practice, some algebraic relations exist between the input and the weights of SDC systems, leading to a singular state space model between the weights and the control input which increases the complexity of the system. The ignorance of time delay in practical systems will make the effectiveness of the fault diagnosis (FD) and fault tolerant control (FTC) be reduced. In this paper, the linear B-spline basis functions are used to approximate the output PDF. A FD approach based on the adaptive observer is established to diagnose the size of fault in the singular time-delayed SDC system. With the fault diagnosis information, a fault tolerant controller based on PI tracking control scheme is constructed to make the post-fault PDF still track the given distribution. The post-fault closed-loop stability analysis with the practical fault tolerant controller is carried out based on the Lyapunov stability theorem. Finally, a numerical simulation is provided to demonstrate the effectiveness of the proposed approach.

Optimal control for discrete-time singular stochastic systems with input delay

Optimal control for discrete-time singular stochastic systems with input delay

Linear Quadratic Nash Game of Stochastic Singular Time-Delay Systems with Multiple Decision Makers

AbstractThis paper discusses linear quadratic Nash game of stochastic singular time-delay systems governed by Itô’s differential equation. Sufficient condition for the existence of Nash strategies is given by means of linear matrix inequality for the first time. Moreover, in order to demonstrate the usefulness of the proposed theory, stochastic H2∕H∞control with multiple decision makers is discussed as an immediate application.

H∞filtering for a class of singular biological systems

This study deals with the H ∞ filtering problem for a class of singular biological systems with stochastic exogenous disturbance. Singular system theory is utilised to build a stochastic singular food chain system. The authors’ purpose is to estimate the unmeasurable state variables of the food chain system by the available measurements. The general condition is established for a class of non-linear singular systems to achieve input-to-state stable in mean and the prescribed H ∞ performance level. A sufficient condition of the solvability of filtering problem is proposed for the singular food chain system. Simulation example is provided to illustrate the effectiveness of the proposed filtering approach developed in this study.

Observer-Based $$H_\infty $$ H ∞ Sliding Mode Controller Design for Uncertain Stochastic Singular Time-Delay Systems

The paper is concerned with the observer-based $$H_\infty $$H? sliding mode controller design for a class of uncertain stochastic singular time-delay systems subjected to input nonlinearity. Using the sliding mode control, a robust law is established to guarantee the reachability of the sliding surface in a finite time interval, and the sufficient condition for asymptotic stability of the error system and sliding mode dynamics with disturbance attenuation level is presented in terms of linear matrix inequalities. Finally, an example illustrates the proposed method.

Distributed Fusion Filter for Multi-rate Sampling Stochastic Singular Systems with Multiplicative Noises

The distributed fusion filtering problem is studied for multi-rate sampling stochastic singular linear systems with multiple sensors and stochastic multiplicative noises. The system is described at the highest sampling rate and different sensors may have different lower sampling rates. The white noise in measurement matrix is introduced to describe the stochastic disturbance. Firstly, based on decomposition in canonical form, the original singular system is transformed into fast and slow two subsystems. For the two reduced-order subsystems, the local filters (LFs) are given based on the “dummy” random variables. The cross-covariance matrices between any two local filtering errors are derived. Further, the distributed fusion filter weighted by matrices (FFWM) is obtained for the original singular system based on the well-known fusion algorithm in the linear minimum variance sense. Simulation example verifies the correctness and feasibility of the proposed algorithm.

Enhanced distributed estimation based on prior information

In this paper, a distributed estimation algorithm using Bayesian-based forward backward Kalman filter (KF) is proposed for stochastic singular linear systems. The method incorporates generalised versions of KF for bounded cases with complete and incomplete prior information, followed by estimation fusion of these cases. The incorporated filters remain optimal given the cross-covariance of the local estimates. The proposed approach is validated on a coupled-tank system.

Fault diagnosis and minimum entropy fault tolerant control for non-Gaussian singular stochastic distribution systems using square-root approximation

The fault diagnosis (FD) and minimum entropy fault tolerant control (FTC) algorithms are proposed for non-Gaussian singular stochastic distribution control (SDC) systems in this paper. Different from general SDC systems, in singular SDC systems, the relationship between the weight vector and the control input is expressed by a singular state space model, which increases the difficulty in the design of fault diagnosis and fault tolerant control. A non-singular state transformation is made to transform the singular dynamic system into a differential-algebraic system. An iterative learning observer (ILO) is designed for fault estimation. The concept of entropy is introduced to fault tolerant control of the non-Gaussian stochastic distribution system when the target probability density function (PDF) is not known in advance. Based on the estimated fault information, the controller is reconfigured by minimising the performance function with regard to the entropy subjected to mean constraint. The reconfigured controller can make the output of the post-fault SDC system still have minimum uncertainty, leading to minimum entropy FTC of the non-Gaussian singular SDC system. Computer simulations are given to demonstrate the validity of the fault diagnosis and minimum entropy FTC algorithms.