Stochastic Singular Systems Research Articles

Intelligent Fuzzy Control with State-Derivative Feedback for Takagi-Sugeno Fuzzy Stochastic Singular Systems

This document deals with the problem of passive fuzzy controller design with the state-derivative feedback approach for the nonlinear stochastic singular systems. Recently, the singular systems have a greater focus on literature because they can keep more physical system characteristics than conventional systems. At first, the Takagi-Sugeno fuzzy stochastic singular models are used to represent the nonlinear stochastic singular systems. Then, the state-derivative feedback approach and parallel distributed compensation method are employed to design the passive fuzzy controllers. In the design process, the Lyapunov stability conditions are developed subject to multiple performance constraints, including the passivity constraint and decay rate constraint. According to these Lyapunov stability conditions, the proposed fuzzy control problem can be effectively shifted into the linear matrix inequality problem that can be solved by using the convex optimal programming algorithm. At last, two examples are provided to verify the applicability and effectivity of the proposed passive fuzzy controller design approach.

New stability criteria for stochastic perturbed singular systems in mean square

In this paper, we investigate the problem of stability of time-varying stochastic perturbed singular systems by using Lyapunov techniques under the assumption that the initial conditions are consistent. Sufficient conditions on uniform exponential stability and practical uniform exponential stability in mean square of solutions of stochastic perturbed singular systems are obtained based upon Lyapunov techniques. Furthermore, we study the problem of stability and stabilization of some classes of stochastic singular systems. Finally, we provide numerical examples to validate the effectiveness of the main results of this paper.

Controllability and Observability of Stochastic Singular Systems in Banach Spaces

Exact (approximate) controllability and exact (approximate) observability of stochastic singular systems in Banach spaces are discussed. Firstly, the condition for the existence and uniqueness of the mild solution to stochastic singular systems is given by GE-semigroup in Banach spaces. Secondly, the necessary and sufficient conditions for the exact (approximate) controllability and exact (approximate) observability of the systems considered are derived in terms of GE-semigroup, and the dual principle is given. Thirdly, an illustrative example is given.

On the Exponential Stability of Stochastic Perturbed Singular Systems in Mean Square

The approach of Lyapunov functions is one of the most efficient ones for the investigation of the stability of stochastic systems, in particular, of singular stochastic systems. The main objective of the paper is the analysis of the stability of stochastic perturbed singular systems by using Lyapunov techniques under the assumption that the initial conditions are consistent. The uniform exponential stability in mean square and the practical uniform exponential stability in mean square of solutions of stochastic perturbed singular systems based on Lyapunov techniques are investigated. Moreover, we study the problem of stability and stabilization of some classes of stochastic singular systems. Finally, an illustrative example is given to illustrate the effectiveness of the proposed results.

Investigation on stability and controller design for singular bio-economic systems with stochastic fluctuations.

In this paper, the finite-time stability and control of a kind of singular bio-economic systems with stochastic fluctuations are investigated. When economic profit is no longer a constant but a variable, the system shows distinct dynamic behavior. First, a singular system is proposed to describe the bio-economic system with stochastic fluctuation. Then a singular stochastic T-S fuzzy model is established based on T-S fuzzy system theory. Second, a sufficient condition is proposed to satisfy finite-time stochastic stability of bio-economic system. On this basis, a fuzzy state feedback controller is designed which can make corresponding closed-loop singular stochastic bio-economic system admissible in finite-time, and the states of the system can be driven to a bounded range through the management of the open resource. Finally, the validity of the results is verified through the numerical simulation.

Mean-Square Admissibility Analysis and Controller Design for Itô-Type Stochastic Singular Systems

The issues of mean-square admissibility and synthesis of It $\hat {o}$ -type stochastic singular systems (SSSs) under Brownian parameter perturbations are introduced in this article. For ease of computation, a novel sufficient condition is given to guarantee autonomous systems are mean-square admissible via strict linear matrix inequalities(LMIs). Furthermore, own to the measurable of the system states, both state feedback controller and observer-based controller (OBC) for It $\hat {o}$ -type SSSs are investigated. However, in It $\hat {o}$ -type SSSs, because the state of the system and the observer can be affected by Brownian fluctuation, it is not feasible that the observer and control gains design are completely separate. To this end, an innovative design approach is also proposed to solve the controller and observer parameters simultaneously in form of strict LMIs. Finally, three examples are introduced to demonstrate the effectiveness of the proposed method.

具有执行器饱和的广义随机系统的滑模自适应控制

具有执行器饱和的广义随机系统的滑模自适应控制

Nonlinear Fault-Tolerant Control Design for Singular Stochastic Systems With Fractional Stochastic Noise and Time-Delay

Nonlinear Fault-Tolerant Control Design for Singular Stochastic Systems With Fractional Stochastic Noise and Time-Delay

Impulse Controllability and Impulse Observability of Stochastic Singular Systems

This paper discusses the impulse controllability and impulse observability of stochastic singular systems. Firstly, the condition for the existence and uniqueness of the impulse solution to stochastic singular systems is given by Laplace transform. Secondly, the necessary and sufficient conditions for the impulse controllability and impulse observability of systems considered are derived in terms of matrix theory. Finally, an example is given to illustrate the effectiveness of the obtained theoretical results.

Fault-Tolerant Control for T-S Fuzzy Stochastic Singular Systems

This article investigates the problem of fault estimation and fault-tolerant control for a class of Takagi–Sugeno fuzzy stochastic singular systems. An integral-type sliding-surface-based augmented singular sliding-mode observer, which is applicable to both dual-normalized and nondual-normalized singular systems, is constructed. It is shown that the restrictive rank condition and the equality constraint can be removed. Then, a sufficient condition in terms of linear matrix inequalities is developed to guarantee the asymptotically mean square admissibility of the closed-loop systems such that the fault can be estimated, and the open-loop system can be stabilized. Moreover, a new adaptive sliding-mode controller is designed such that the reachability condition can be guaranteed. Finally, two examples are presented to verify the effectiveness of the proposed method.

Integral sliding mode control for T–S fuzzy descriptor systems

The present study focuses on designing the integral sliding-mode control (ISMC) for generalized Takagi–Sugeno (T–S) fuzzy singular stochastic systems by involving the Markovian jump type of system parameters. Distinct to the existing works, the present paper concerns about the derivation of sufficient conditions that ensure the global stability of considered T–S fuzzy stochastic singular Markovian jump systems with matched/mismatched uncertainties under fuzzy-based ISMC. In this regard, an improved fuzzy integral sliding manifold function with mode-dependent derivative-term coefficient is proposed where the matched uncertainties become unnecessary and the mismatched uncertainties have been disintegrated during the sliding mode phase. Based on Lyapunov stability theory, a suitable Lyapunov functional candidate by involving the information about the membership functions is constructed with singular and P-type matrices, the stochastic admissibility of corresponding sliding mode dynamics are derived. To proven the effectiveness of the proposed method, a physical experimental problem on cart and pendulum is adapted and simulated via the derived theoretical results and the corresponding results are provided.

Admissibility analysis of stochastic singular systems with Poisson switching

This paper addresses the mean square admissibility problem for a class of stochastic singular systems with Poisson switching. By using H-representation approach, we show the equivalence between mean square admissibility and robust admissibility of a deterministic system, which is an extension of the result in the case of deterministic system [1]. Based on multiple Lyapunov functions and matrix decomposition approaches, some easily verifiable sufficient conditions without equality constraint are established and can be conveniently used to state feedback controller design. Some admissibility criteria are constructed for linear singular systems with Poisson switching. Three examples including a RLC circuit and a mass-spring-damper system are introduced to demonstrate the validity of the theoretical results.

An exact null controllability of stochastic singular systems

An exact null controllability of stochastic singular systems

Stability analysis for semi-Markovian switched singular stochastic systems

The stability problem is investigated for switched singular stochastic systems with semi-Markovian switching signals. Considering the inherent mode-dependent state jumps at the switching instants, sufficient conditions of stochastic stability, exponential stability in the mean square and almost surely exponential stability are obtained by using the stochastic analysis theory and Lyapunov function method. Finally, an example is provided to illustrate the effectiveness of the proposed results.

H∞ Control for Stochastic Singular Systems With Time-Varying Delays

In this article, we study the H ∞ control problems for stochastic singular systems with time-varying delays. Firstly, a new Lyapunov-Krasovskii functional is constructed, employing the free weighting matrix technique and Jensen inequality, the stochastic admissibility criteria in the mean square for stochastic singular time-varying delay systems are proposed on the basis of the auxiliary vector function. Secondly, the state feedback controller is designed such that the resulting closed-loop system meets regular, impulse-free, stochastically stable in the mean square and has H ∞ performance γ. In the proof process, the dual equation is used to derive the conditions of stochastic admissibility in the mean square. Finally, a practical example of DC motor model is presented to show the validity of our proposed theoretical results.

On Positive Realness for Stochastic Hybrid Singular Systems

This paper deals with the problem of passivity analysis and passivity-based synthesis for continuous-time stochastic hybrid singular systems (SHSSs). First, a set of linear matrix inequalities for the stochastic admissibility and passivity, which is also known as the positive real lemma, is obtained for continuous-time SHSSs. The proposed condition successfully holds a necessary and sufficient condition for the positive realness of SHSSs, whereas the existing papers in the literature have been handled only sufficient conditions. Next, the passivity-based control synthesis problem is also considered based on the new positive real lemma. The passivity-based stabilization criterion for the closed-loop system with its mode-dependent state-feedback control is expressed in terms of matrix inequality. Thus, by introducing an additional slack matrix to the non-convex conditions, the feasible conditions for the control gain are obtained in terms of linear matrix inequalities. Finally, a numerical example is provided to show the effectiveness of the result.

Preview control for continuous-time singular stochastic systems

In this paper, the problem of preview control for continuous-time singular stochastic systems is studied by the augmented error system approach. First, a static output feedback is introduced to make the closed-loop system impulse-free. And through the second restricted equivalent transformation, the continuous-time singular stochastic system is transformed into a normal stochastic system and some algebra equations. Then, an assistant system is designed to overcome the difficulty of trying to make derivation to a stochastic system like in deterministic system condition. And the stochastic system after the transformation is translated to the assistant system. In order to make the output of the singular system track the reference signal as accurately as possible without static error, an integrator is introduced. Based on the system after the translation and the error equation, an augmented error system is constructed with the state vector, the error vector and the reference signal. Finally, the tracking problem for the singular stochastic system is transformed into the optimal regulating problem for the augmented error system. By the dynamic programming method, the optimal preview controller for the original singular stochastic system is obtained. The existence and uniqueness solution of the Riccati equation is discussed and the numerical analysis shows the effectiveness for the preview controller designed in this paper.

WMF self-tuning Kalman estimators for multisensor singular system

For the multisensor linear stochastic singular system with unknown noise variances, the weighted measurement fusion (WMF) self-tuning Kalman estimation problem is solved in this paper. The consistent estimates of these unknown noise variances are obtained based on the correlation method. Applying the WMF method and the singular value decomposition (SVD) method yields the WMF reduced-order subsystems. Based on these consistent estimates of unknown noise variances and the new non-singular systems, the WMF self-tuning Kalman estimators of the state components and white noise deconvolution estimators are presented. Then the WMF self-tuning Kalman estimators of the original state are presented, and their convergence has been proved by dynamic error system analysis (DESA) method and dynamic variance error system analysis (DVESA) method. A simulation example of 3-sensors circuits systems verifies the effectiveness, the accuracy relationship and the convergence.

Finite-time H∞ Control of Stochastic Singular Systems with Partly Known Transition Rates via an Optimization Algorithm

This paper is concerned with the problem of finite-time H∞ control for stochastic singular systems with partly known transition rates (TRs). The transition of system parameters follows a finite-state Markov process. Firstly, based on stochastic functional method and linear matrix inequalities (LMIs) technique, sufficient conditions are proposed to ensure finite-time stochastic boundedness (FTSB) and finite-time H∞ stochastic boundedness (FTH∞SB) of considered stochastic singular system. Secondly, by designing a state feedback controller, strict LMI conditions are obtained to guarantee the closed-loop system with partly known TRs to be FTSB and FTH∞SB. Finally, a numerical example is provided to demonstrate the effectiveness of the proposed methods.

Near-optimal control for a singularly perturbed linear stochastic singular system with Markovian jumping parameters

In this paper, we investigate the near-optimal control for a singularly perturbed linear stochastic singular system with Markovian jumping parameters. Firstly, we warrant the given system has an impulse-free solution. Secondly, by means of the singular value decomposition, the existence of solution are obtained for the singularly perturbed stochastic generalized coupled differential Riccati equation and establish an existence of solution to parameter-independent system for the stochastic generalized coupled differential Riccati equation. As an application, we apply the existence results to consider the near-optimal control of singularly perturbed linear stochastic singular system with Markovian jumping parameters, and obtain the desired explicit representation of the optimal controllers for the optimal control problem with the finite horizon.