非线性随机时滞系统的稳定性与应用

首先考虑了不确定性的一族非线笥随机时滞系统,建立了这种系统的均方指数稳定与几乎必须指数稳定的充分准则,其准则是时滞无关的,然后应用这些充分条件到一类不确定的随机时滞神经网络,得到了这咱神经网络指数稳定的产用判据。本文的结果是最近文献中某些结果的推广,最后一个数值例子说明的所给准则的有效性。     

非线性滞后It(?)随机系统的滞后无关均方渐近稳定性

研究非线性滞后Ito随机系统的滞后无关均方渐近稳定性,将关于线性时滞不等式的Halanay不等式推广到非线性情形,用Lyapunov函数和关于时滞随机系统的比较原理,得到了非线性滞后Ito随机系统滞后无关均方渐近稳定性的一些判据。     

具有非线性滞后关联的随机大系统的分散镇定

本文通过利用李雅普诺夫函数和李雅普诺夫矩阵方程的性质，对具有非线性滞后关联的一类随机大系统建立了分散鲁棒镇定的判据，所得闭环随机大系统的和稳定性不依赖于任意实数滞后，并对不确定系数矩阵和随机扰动强度具有鲁棒性。     

时滞随机大系统的分散次优镇定

本文基于Ｒｉｃａａｔｉ矩阵方程、采用Ｌｙａｐｕｎｏｖ泛函研究具有时滞的Ｉｔｏ型随机大系统的分散次优镇定，建立了分散次优镇定的判据，给出了确定分散次优控制器的一个算法，这个算法以求解Ｌｙａｐｕｎｏｖ矩阵方程与Ｒｉｃｃａｔｉ矩阵方程为基础。文中命同了数值算例以说明本文算法的用法。     

Controllability of nonlinear systems consisting of a bilinear mode with time-varying delays in control

Sufficient conditions are established for the global relative controllability of nonlinear system consisting of a bilinear mode with time-varying delays in control. The results are a generalization of previous results and are obtained by using Schauder's fixed point theorem.     

Controllability of Singularly Perturbed Linear Time-Dependent Systems with Small State Delay

A singularly perturbed linear time-dependent control system with multiple point and distributed small delays in state variables is considered. Two lower-dimension systems (the reduced-order and the boundary-layer ones), associated with the original system, are introduced. The reduced-order and the boundary-layer systems are in separate time scales, and they do not contain the small parameter any more. Connections between the properties of controllability of these systems and such a property of the original system itself are established for all sufficiently small values of the parameter of singular perturbations.     

Memoryless SMC Design Methods for Stochastic Delay Systems

Recently, the sliding mode control (SMC) method has been extended to accommodate stochastic systems. Particularly, restrictive assumption on the structure of the control systems have been removed and a practical SMC design method for stochastic systems has been presented. This paper continues this line of research and studies the SMC methods for stochastic systems with state delay in diffusion. Both delay‐independent and delay‐dependent approaches are investigated. Essentially, this paper studies SMC design methods with memoryless controllers for time delay systems, which has been a problem in the past decades.     

Controllability of Fractional Order Stochastic Differential Inclusions with Fractional Brownian Motion in Finite Dimensional Space

In this paper, sufficient conditions are formulated for controllability of fractional order stochastic differential inclusions with fractional Brownian motion (fBm) via fixed point theorems, namely the Bohnenblust-Karlin fixed point theorem for the convex case and the Covitz-Nadler fixed point theorem for the nonconvex case. The controllability Grammian matrix is defined by using Mittag-Leffler matrix function. Finally, a numerical example is presented to illustrate the efficiency of the obtained theoretical results.      

具有区间时滞的不确定性随机时滞系统的时滞相关鲁棒稳定性

针对具有区间时滞的不确定性随机时滞系统, 进行稳定性分析. 通过考虑变时滞、时滞的上界及它们的差三者之间的关系, 并应用公式和Lyapunov稳定性理论, 在不忽略任何有用项的前提下, 得到改进的具有区间时滞的随机系统的稳定性判据. 数值实例验证了该方法的有效性.     

网络控制系统中随机传输时延的预测补偿研究

This paper proposes a predictive compensation strategy to reduce the detrimental effect of stochastic time delays induced by communication networks on control performance. Values of a manipulated variable at the present sampling instant and future time instants can be determined by performing a receding horizon optimal procedure only once. When the present value of the manipulated variable does not arrive at a smart actuator, its predictive one is imposed to the corresponding process. Switching of a manipulated variable between its true present value and the predictive one usually results in unsmooth operation of a control system. This paper shows: 1) for a steady process, as long as its input is sufficiently smooth, the smoothness of its output can be guaranteed; 2) a manipulated variable can be switched smoothly by filtering the manipulated variable just using a simple low-pass filter. Thus the control performance can be improved. Finally, the effectiveness of the proposed method is demonstrated by simulation study.     

Predictive Compensation for Stochastic Time Delay in Network Control Systems

This paper proposes a predictive compensation strategy to reduce the detrimental effect of stochastic time delays induced by communication networks on control performance. Values of a manipulated variable at the present sampling instant and future time instants can be determined by performing a receding horizon optimal procedure only once. When the present value of the manipulated variable does not arrive at a smart actuator, its predictive one is imposed to the corresponding process Switching of a manipulated variable between its true present value and the predictive one usually results in unsmooth operation of a control system. This paper shows: 1) for a steady process, as long as its input is sufficiently smooth, the smoothness of its output can be guaranteed; 2) a manipulated variable can be switched smoothly by filtering the manipulated variable just using a simple low-pass filter. Thus the control performance can be improved. Finally, the effectiveness of the proposed method is demonstrated by simulation study.     

State‐Feedback Stabilization of Stochastic Nonlinear Systems with Time‐Varying Delay and Different Orders

This paper studies the problem of state feedback stabilization for a class of stochastic time‐varying delay nonlinear systems which are neither necessarily feedback linearizable nor affine in the control input. Based on the backstepping design method and the adding of a power integrator technique, a state feedback controller is constructed to ensure the origin of closed‐loop system is globally asymptotically stable in probability. The main design difficulty is how to deal with the different power orders, time‐varying delay and the nonsmooth system perturbations. The efficiency of the state feedback controller is demonstrated by a simulation example.     

Disturbance Decoupling of Time Delay Systems

A necessary and sufficient condition is derived for the solvability of the disturbance decoupling problem by a pure shift dynamic compensator. It corrects previously obtained results for multi‐input multi‐output (MIMO) systems. Also, necessary and sufficient conditions are given for the solvability of the problem by a dynamic compensator for single input single output (SISO) systems.     

Adaptive Neural Dynamic Surface Control for Stochastic Nonlinear Time‐Delay Systems with Input and Output Constraints

This paper presents an adaptive neural tracking control approach for uncertain stochastic nonlinear time‐delay systems with input and output constraints. Firstly, the dynamic surface control (DSC) technique is incorporated into adaptive neural control framework to overcome the problem of ‘explosion of complexity’ in the control design. By employing a continuous differentiable asymmetric saturation model, the input constraint problem is solved. Secondly, the appropriate Lyapunov‐Krasovskii functional and the property of hyperbolic tangent functions are used to deal with the unknown time‐delay terms, RBF neural network is utilized to identify the unknown systems functions, and barrier Lyapunov functions (BLFs) are designed to avoid the violation of the output constraint. Finally, based on adaptive backstepping technique, an adaptive neural control method is proposed, and it decreases the number of learning parameters. Using Lyapunov stability theory, it is proved that the designed controller can ensure that all the signals in the closed‐loop system are 4‐Moment (or 2 Moment) semi‐globally uniformly ultimately bounded (SGUUB) and the tracking error converges to a small neighborhood of the origin. Two simulation examples are provided to further illustrate the effectiveness of the proposed approach.     

On the Controllability of Nonlocal Second‐Order Impulsive Neutral Stochastic Integro‐Differential Equations with Infinite Delay

In this paper, we investigate the controllability for a class of nonlocal second‐order impulsive neutral stochastic integro‐differential equations with infinite delay in Hilbert spaces. More precisely, a set of sufficient conditions for the controllability results of nonlocal second‐order impulsive neutral stochastic integro‐differential equations with infinite delay are derived by means of the Banach fixed point theorem combined with theories of a strongly continuous cosine family of bounded linear operators. As an application, an example is provided to illustrate the obtained theory.     

一类时滞非线性控制系统的输出调节

研究了一类单输出时滞线性系统的输出调节问题,首先通过精确线性化方法将其转化为一类特殊线性时滞系统对非线系统的跟踪总是,然后通过积分变换转化为无时滞的线性系统对非线性系统的跟踪,新的精确线性化结果保证了经过积分变换后的系统仍然可控,同时,提出了可解性的概念解决了线性系统对非线性系统的跟踪问题,得到了时滞非线性系统输出调节问题的局部和全局的结果,该结果对外部系统假设较弱。     

Robust Stochastic Stability for a Class of Singular Systems with Uncertain Markovian Jump and Time‐Varying Delay

This paper deals with the problem of the robust stochastic stability for a class of singular systems with uncertain Markovian jump and time‐varying delay. Sufficient conditions on the stochastic stability are presented. The obtained results are formulated in terms of strict linear matrix inequalities. A numerical example is provided to show the effectiveness of the proposed approaches.     

Stochastic controllability of linear systems with Markovian jumps

The notion of stochastic controllability for linear systems subject to Markovian jumps in parameter values is studied. An algebraic necessary and sufficient condition is obtained in terms of an easily computable rank test.     

一种随机Petri网模拟系统时延分析的新方法*

本文首先引入了时延网和闭网的概念,证明了Petri网N为时延网的充要条件是其闭网为常返网;然后,从时延网模型出发,讨论了变迁发射时间为任意分布的随机离散事件系统时延特性的求取方法,给出了时延密度的计算公式。     

Controllability for Discrete Systems with a Finite Control Set

In this paper we consider the problem of controllability for a discrete linear control system x _k+1=Ax _k+Bu _k, u _k∈U, where (A,B) is controllable and U is a finite set. We prove the existence of a finite set U ensuring density for the reachable set from the origin under the necessary assumptions that the pair (A,B) is controllable and A has eigenvalues with modulus greater than or equal to 1. In the case of A only invertible we obtain density on compact sets. We also provide uniformity results with respect to the matrix A and the initial condition. In the one-dimensional case the matrix A reduces to a scalar λ and for λ>1 the reachable set R(0,U) from the origin is?