随机多智能体系统稳定性综述

随机多智能体系统一致稳定性分析大致可区分为: 带随机噪声的多智能体系统的一致稳定性分析, 切换拓扑下随机多智能体系统一致稳定性分析, 随机时滞多智能体系统一致稳定性分析, 随机多智能体系统分布式优化控制一致稳定性分析. 对此, 从以上4 个方面对随机多智能体系统稳定性问题的研究进展及其存在的问题进行阐述, 并对随机多智能体系统一致稳定性的进一步研究方向进行了展望.

     

Stability preserving mappings for stochastic dynamical systems

We first formulate a general model for stochastic dynamical systems that is suitable in the stability analysis of invariant sets. This model is sufficiently general to include as special cases most of the stochastic systems considered in the literature. We then adapt several existing stability concepts to this model and we introduce the notion of stability preserving mapping of stochastic dynamical systems. Next, we establish a result which ensures that a function is a stability preserving mapping, and we use this result in proving a comparison stability theorem for general stochastic dynamical systems. We apply the comparison stability theorem in the stability analysis of dynamical systems determined by Ito differential equations     

Stability of stochastic composite systems

In a recent paper [15] results for the asymptotic stability and exponential stability (with probability one) of a class of continuous parameter stochastic composite systems, with disturbances confined to the sub-system structure, were established. In this short paper these results are extended to allow stability analysis of systems for which stochastic disturbances may not only enter into the subsystem structure but also into the interconnecting structure of composite systems. As in previous related results, the objective is to analyze composite systems in terms of their lower order subsystems and in terms of their interconnecting structure.     

Finite-time stability and instability of stochastic nonlinear systems

This paper presents a new definition of finite-time stability for stochastic nonlinear systems. This definition involves stability in probability and finite-time attractiveness in probability. An important Lyapunov theorem on finite-time stability for stochastic nonlinear systems is established. A theorem extending the stochastic Lyapunov theorem is also proved. Moreover, an example and a lemma are presented to illustrate the scope of extension. A useful inequality, extended from Bihari’s inequality, is derived, which plays an important role in showing the Lyapunov theorem. Finally, a Lyapunov theorem on finite-time instability is proved, which states that almost surely globally asymptotical stability is not equivalent to finite-time stability for some stochastic systems. Two simulation examples are given to illustrate the theoretical analysis.     

灰色随机线性时滞系统的渐近稳定性

首先提出了灰色随机线性时滞系统及其渐近稳定性的概念;然后,利用矩阵理论和随机微分时滞方程解的渐近收敛定理及李雅普诺夫函数,研究了灰色随机线性时滞系统的渐近稳定性,得到了随机淅近稳定的几个充分性条件;最后,通过数值例子说明了所得结果在实际应用中的方便性和有效性.     

Optimal tracking design for stochastic fuzzy systems

In general, fuzzy control design for stochastic nonlinear systems is still difficult since the fuzzy bases are stochastic so as to increase the difficulty and complexity of the fuzzy tracking control design. In this study, a fuzzy stochastic moving-average model with control input (fuzzy ARMAX model) is introduced to describe nonlinear stochastic systems. From the fuzzy ARMAX model, a fuzzy one-step ahead prediction model is developed. Based on a fuzzy one-step ahead prediction stochastic model, optimal design algorithms are proposed to achieve the optimal tracking of nonlinear stochastic systems. In this study, the minimum variance tracking control, generalized minimum variance tracking control, and the optimal model reference tracking control are developed for stochastic fuzzy systems. We construct some basic stability conditions for general stochastic fuzzy systems and use these conditions to verify the stability of the fuzzy tracking control systems. Finally, two simulation examples are given to indicate the performance of the proposed methods.     

Stochastic input-to-state stability of switched stochastic nonlinear systems

In this paper, global asymptotic stability in probability (GASiP) and stochastic input-to-state stability (SISS) for nonswitched stochastic nonlinear (nSSNL) systems and switched stochastic nonlinear (SSNL) systems are investigated. For the study of GASiP, the definition which we considered is not the usual notion of asymptotic stability in probability (stability in probability plus attractivity in probability); it can depict the properties of the system quantitatively. Correspondingly, based on this definition, some sufficient conditions are provided for nSSNL systems and SSNL systems. Furthermore, the definition of SISS is introduced and corresponding criteria are provided for nSSNL systems and SSNL systems. In the proof of the above results, to overcome the difficulties coming with the appearance of switching and the stochastic property at the same time, we generalize the past comparison principle and fully use the properties of the functions which we constructed. In terms of the average dwell-time of the switching laws, a sufficient SISS condition is obtained for SSNL systems. Finally, some examples are provided to demonstrate the applicability of our results.     

Frequency domain stability criteria for stochastic systems

The stability of a class of dynamical systems containing random parameters is investigated. An input-output stability concept is formulated for stochastic systems. The specific class of systems considered consists of those feedback systems whose open loop consists of the cascade of a white noise multiplicative gain and a linear deterministic dynamical system. Necessary and sufficient frequency domain conditions for stability are derived and it is shown that the uncertainty has a destabilizing effect. The resulting stability conditions depend on the open-loop stability, the rms value of the stochastic gain element, and the effective bandwidth of the linear element.     

The asymptotic stochastic stability in large of the composite stochastic systems

The sufficient conditions of asymptotic stochastic stability in large of non-linear composite stochastic systems are established. In this case the objective is to analyze composite systems in their lower order subsystems and in terms of their interconnecting structure. Non-linear systems are considered, with random noise which obeys the law of large numbers. An example is given to illustrate the criteria.     

具有可变时滞的中立型随机系统的渐近性质

本文研究了一类具有可变时滞的中立型随机系统解的渐近性质.利用Lyapunov函数It、^o公式和上鞅收敛定理,得到了该系统解的一些几乎必然渐近稳定性与p阶均值渐近稳定性、几乎必然多项式渐近稳定性与p阶均值多项式渐近稳定性及几乎必然指数稳定性与p阶均值指数稳定性的充分判据.与经典的随机稳定性结论相比,本文所建立的判据充分利用了随机扰动项的作用,无须LV(扩散算子)的负定.     

Delay-dependent robust stability of stochastic delay systems with Markovian switching

In recent years, the stability of hybrid stochastic delay systems, one of the important issues in the study of stochastic systems, has received considerable attention. However, the existing results do not deal with the structure of the diffusion but estimate its upper bound, which induces conservatism. This paper studies delay-dependent robust stability of hybrid stochastic delay systems. A delay-dependent criterion for robust exponential stability of hybrid stochastic delay systems is presented in terms of linear matrix inequalities （LMIs）, which exploits the structure of the diffusion. Numerical examples are given to verify the effectiveness and less conservativeness of the proposed method.     

Stability analysis and stabilization control of multi-variable switched stochastic systems

In this paper, the mean square (MS) stability and exponential mean square (EMS) stability of multi-variable switched stochastic systems are investigated. Based on the concept of the average dwell-time and the ratio of the total time running on all unstable subsystems to the total time running on all stable subsystems, some sufficient conditions are given to ensure the MS stability and EMS stability of the switched stochastic systems involved. Further, for the switched stochastic control systems with all subsystems controllable or stabilizable, EMS stabilization controls and sufficient conditions on EMS stabilization are presented, and the convergent rates of the closed-loop systems are obtained.     

时滞非线性随机大系统的指数稳定性

建立了一般随机泛函微分方程p阶均值指数稳定与几乎必然指数稳定的新型判据, 然后应用所得判据到具有可变多时滞的非线性随机大系统, 得到了这种随机大系统时滞无关的均方指数稳定与几乎必然指数稳定的代数判据.     

Exponential stability of stochastic delay interval systems

Although deterministic interval systems have received a great deal of attention, so far there is no work on stochastic interval systems. The main aim of this paper is to initiate the study of stochastic interval systems. Of course, there are many properties of such systems to be investigated, but this paper will concentrate on the study of exponential stability of stochastic interval systems with time-varying delays. The main technique used in this paper is the Razumikhin-type theorem established recently by Mao (Stochastic Process. Appl. 65 (1996) 233–250).     

Exponential stability of stochastic systems with hysteresis switching

For stochastic systems with state-dependent switching which are motivated by active regions of subsystems, the exponential stability is studied in this paper. Distinct from most of the existing references, the existence of the solution to stochastic switched systems is not given as a priori information but can be proved under some easily verified conditions. By the aid of Dynkin’s formula, Itô’s formula and exponential martingale inequality, the criteria on moment exponential stability and almost sure exponential stability of the stochastic switched system are established based on Lyapunov-like techniques. Simulation examples are presented to illustrate the validity of the results.     

Stabilization for T-S model based uncertain stochastic systems

This paper considers the stabilization problem of a class of uncertain Itô stochastic fuzzy systems driven by a multidimensional Wiener process. The uncertainty modeled in the systems is of the linear fractional type which includes the norm-bounded uncertainty as a special case. The objective is to design a state-feedback fuzzy controller such that the closed-loop system is robustly asymptotically stable under a stochastic setting. By using a stochastic Lyapunov approach, sufficiency conditions for the stability and stabilization of this class of systems are established based on a novel matrix decomposition technique. The derived stability conditions are then employed to design controllers which stabilize the uncertain Itô stochastic fuzzy systems. Two simulation examples are given to illustrate the effectiveness of the approaches proposed.     

Stability analysis of stochastic composite systems

New results for asymptotic stability and exponential stability with probability one of several classes of continuous parameter and discrete parameter stochastic composite systems are established. In all cases the objective is to analyze composite systems in terms of their lower order subsystems and in terms of their interconnecting structure. The results are applied to three specific examples.     

Asymptotic stability in distribution of stochastic systems with semi-Markovian switching

This paper investigates the asymptotic stability in distribution of stochastic systems with semi-Markovian switching whose transition rates are time varying, which are more general than stochastic systems with Markovian switching. Some sufficient conditions for the asymptotic stability in distribution of stochastic systems with semi-Markovian switching are established and those conditions are employed to design the state-feedback controllers in terms of linear matrix inequalities. Finally, several examples are given to illustrate the effectiveness of the theoretical results.     

Robust delayed-state-feedback stabilization of uncertain stochastic systems

Due to time spent in computation and transfer, control input is usually subject to delays. Problems of deterministic systems with input delay have received considerable attention. However, relatively few works are concerned with problems of stochastic system with input delay. This paper studies delayed-feedback stabilization of uncertain stochastic systems. Based on a new delay-dependent stability criterion established in this paper, a robust delayed-state-feedback controller that exponentially stabilizes the uncertain stochastic systems is proposed. Numerical examples are given to verify the effectiveness and less conservativeness of the proposed method.     

Robust design of stochastic controllers for nonlinear systems

The previous results are generalized on the stabilizing property of a control scheme designed for a class of discrete-time nonlinear stochastic systems. First, the existing controller is made more robust with a prescribed degree of stability by proper modifications. Next, the inherent robustness is illustrated by a design utilizing erroneous noise characteristics. Reconsideration of the stability analysis used allows one to treat a larger class of nonlinear stochastic systems with more general structures