随机系统输出概率密度函数的有限时间镇定

针对一类含有限能量未知扰动的随机动态系统,研究基于随机分布函数的有限时间控制问题．通过Ｂ 样条逼近建立了输出概率密度函数（ＰＤＦ）与权值之间的对应关系,利用线性矩阵不等式,给出了基于观测器的ＰＤＦ 有限时间控制器的参数化设计方法．采用该方法设计的控制器,可使系统对所有满足条件的未知扰动是随机有限时间有界和随机有限时间镇定的．仿真实例验证了所提出方法的有效性．

     

Markov跳变系统的有限时间状态反馈镇定

讨论一类含有限能量未知扰动的线性Markov跳变系统的有限时间镇定问题.针对连续系统和离散系统两种情况,利用构造的Lyapunov-Krasovskii函数,并结合线性矩阵不等式方法,分别证明并给出了跳变系统有限时间镇定控制器有解的充分条件.采用该方法设计的镇定控制器可使连续系统和离散系统对所有满足条件的未知扰动是有限时问有界和有限时间镇定的.最后通过数值示例表明了该设计方法的有效性.     

一类线性离散时间系统有限时间控制问题

讨论一类具有时变、有限能量外部扰动的线性离散时间系统的有限时间控制问题.首先研究问题可解的充分条件,并讨论了状态反馈控制器存在的条件,这些条件可归结为基于线性矩阵不等式(LMI)的可解性问题;然后给出状态反馈控制器和输出反馈控制器的具体设计;最后通过仿真验证了该方案的有效性.     

线性随机系统有限时间H∞ 控制

讨论一类具有时变、有限能量外部扰动的线性随机系统有限时间H∞控制问题．首先,给出了线性随机系统有限时间如控制问题的定义;然后,通过构造Lyapunov-Krasovskii函数,并结合线性矩阵不等式,给出了随机系统有限时间如控制器有解的充分条件;进一步,将该问题简化为具有线性矩阵不等式约束的优化问题,并给出了相应的求解算法;最后,通过数值算例表明了该设计方法的有效性．     

基于LMI的大型互联线性系统的分散有限时间镇定

借助于有限时间稳定性的定义,针对大型互联线性系统,引入了分散有限时间镇定的概念.对一类大型互联线性系统进行分散状态反馈和分散动态输出反馈控制器设计,利用线性矩阵不等式(LMI)的方法提出一个充分条件,当反馈控制律作用于该系统时,闭环系统是有限时间稳定的.仿真算例说明了所得结论的可行性和有效性.     

不确定奇异系统的有限时间H_∞控制

针对一类在有限时间下的线性奇异系统,同时考虑参数不确定性和有限外部扰动影响,研究了系统基于状态反馈控制器的鲁棒H∞控制问题。首先通过构造合适的Lypunov函数,利用线性矩阵不等式方法给出了线性广义系统有限时间有界且H∞范数有界的充分条件,在此基础上讨论线性广义系统的H∞状态反馈控制,给出了控制器存在的充分条件,同时给出了控制器的具体设计方法,控制器可由线性矩阵不等式解得。最后的数值算例说明了所提出方法的可行性和有效性。     

基于谱技术的随机系统的区间输出反馈镇定控制

基于谱技术研究了线性随机系统的区间稳定性与镇定控制问题.首先给出了保证随机系统区间稳定的充分性判据,该判据可确保随机系统的谱全部位于左半复平面的某一带状区域内;然后,利用矩阵的奇异值分解给出了静态输出反馈镇定控制器的设计方法,并将其归结为一组线性矩阵不等式（LMIs）的求解问题;最后,数值仿真验证了所得结论的正确性.     

一类非线性随机不确定系统有限时间H∞无穷滤波

研究一类具有时变、有界干扰的非线性随机不确定系统有限时间H∞滤波问题.首先,给出了非线性随机不确定系统有限时间H∞滤波问题的定义;其次,通过构造Lyapunov-Krasoviskii函数,并结合线性矩阵不等式（LMI）方法,给出了非线性随机不确定系统有限时间∞滤波器存在的充分条件;再次,将该问题简化为具有LMI约束的优化问题,并给出了相应的求解算法;最后,通过数值算例表明了所提出设计方法的有效性.     

具有外部扰动的离散广义系统有限时间控制

讨论一类具有有限能量的外部扰动的线性离散广义系统的有限时间控制问题。分析问题可解性,得到该问题可解的充分条件,通过状态反馈控制器和输出反馈控制器的设计,给出实现闭环系统有限时间有界的充分条件,这些充分条件可以转化为线性矩阵不等式(LMI)的可行解问题,可借助Matlab中的LMI工具箱求解,最后通过数值算例验证该方法的...     

一类不确定线性时滞系统的输出反馈鲁棒镇定

研究一类不确定线性时滞系统的输出反馈鲁棒镇定问题,其中不确定性不必满足匹配条件。以二次Lyapunov泛函保证系统的渐近稳定性,利用线性矩阵不等式给出了系统可以利用动态输出反馈鲁棒镇定的充分条件。当此条件成立时,基于线性矩阵不等式的解构造了全阶动态输出反馈镇定控制器。     

Robust stabilization of stochastic differential inclusion systems with time delay

This paper is concerned with robust stabilization of stochastic differential inclusion systems with time delay.A nonlinear feedback law is established by using convex hull quadratic Lyapunov function s...     

Optimal probability density function control for NARMAX stochastic systems

This paper presents a new control strategy for a class of non-Gaussian stochastic systems so that the output probability density function (PDF) of the system can be made to follow a desired PDF. The system considered is represented by an Nonlinear AutoRegressive and Moving Average with eXogenous (NARMAX) inputs with input channel time-delay and non-Gaussian noise. A multi-step-ahead nonlinear cumulative cost function is used to improve tracking performance. For this purpose, a relationship between the PDFs of all the inputs and the PDFs of multiple-step-ahead output is formulated by constructing an auxiliary multivariate mapping. By minimizing this performance function, a new explicit predictive controller design algorithm is established with less conservatism than some previous results. Furthermore, an improved approach is developed to guarantee the local stability of the closed-loop system by tuning the weighting parameters recursively. Simulations are given to demonstrate the effectiveness of the proposed control algorithm and desired results have been obtained.     

Global mean‐square exponential stabilization of stochastic system with time delay via impulsive control

This paper discusses the global mean‐square exponential stabilization problem for a class of nonlinear non‐autonomous stochastic systems with time delay via impulsive controller. By employing the D‐measure of the matrix and establishing a formula for the variation of parameters, some sufficient conditions are proposed for the design of an impulsive controller such that the stochastic impulsive control system with time varying system matrix and time delay is globally mean‐square exponentially stable. Some numerical examples are presented to illustrate the effectiveness of the proposed results. Copyright © 2011 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

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.     

马尔可夫链中首次到达时间概率密度函数值的简化计算

为了简化马尔可夫链中首次到达时间概率密度函数值的计算,构造一个图的矩阵表示产生的有向图,形象地得出从一个状态首次到达另一个状态的所有路径．该问题被转化为对所有满足从一个状态首次到达另一个状态的情况概率值的累加．在此基础上利用所要解决的问题提供的1步平稳转移概率计算出从一个状态到另一个状态的首次到达时间的概率密度函数值．此方法不仅更加直观地计算出此函数值,免去记忆复杂的通用公式,而且省去在公式中为计算此函数值所做的在1步平稳转移概率的基础上再次计算n步平稳转移概率的计算工作.特别是在n较小的情况下,采用此方法进行手工计算比用公式法快捷且易于理解,因此体现出明显的优势．     

随机非线性时滞大系统的输出反馈分散镇定

针对具有严格反馈形式的随机非线性时滞大系统,设计了含有时滞项的随机控制Lyapunov函数,运用Backstepping技术,构造出一类输出反馈无记忆控制器.在此控制器作用下,所考虑的闭环系统实现概率意义上的时滞无关全局渐近稳定.并在无限时区优化指标函数的约束下,对控制器进行逆优再设计,以满足一定的性能要求.     

随机部分可积拟哈密顿系统的概率密度追踪控制

目前非线性随机系统的控制方法存在设计复杂,计算成本高,以及缺乏稳定性或收敛性证明等缺点,针对这些问题,本文在作者前期研究的基础上发展了一种全新的针对部分可积的非线性随机系统的反馈控制,使得受控系统输出的稳态概率密度逼近事先给定的目标概率密度,并利用Lyapunov函数法证明受控系统的收敛性.数学仿真结果证明了这种方法的可行性和正确性.     

Delay-dependent stabilization of stochastic interval delay systems with nonlinear disturbances

In this paper, a delay-dependent approach is developed to deal with the robust stabilization problem for a class of stochastic time-delay interval systems with nonlinear disturbances. The system matrices are assumed to be uncertain within given intervals, the time delays appear in both the system states and the nonlinear disturbances, and the stochastic perturbation is in the form of a Brownian motion. The purpose of the addressed stochastic stabilization problem is to design a memoryless state feedback controller such that, for all admissible interval uncertainties and nonlinear disturbances, the closed-loop system is asymptotically stable in the mean square, where the stability criteria are dependent on the length of the time delay and therefore less conservative. By using Itô's differential formula and the Lyapunov stability theory, sufficient conditions are first derived for ensuring the stability of the stochastic interval delay systems. Then, the controller gain is characterized in terms of the solution to a delay-dependent linear matrix inequality (LMI), which can be easily solved by using available software packages. A numerical example is exploited to demonstrate the effectiveness of the proposed design procedure.     

Dwelling time probability density distribution of instances in a workflow model

This paper presents a method to judge whether a business process is successful or not. A business process is deemed successful if a large enough proportion of instances dwell in a workflow (wait and be executed) for less than given period. By analyzing instances’ dwelling time distribution in a workflow, the proportion of instances which dwell in the workflow for less than any given period will be achieved. The performance analysis of workflow model plays an important role in the research of workflow techniques and efficient implementation of workflow management. It includes the analysis of instances’ dwelling time distribution in a workflow process. Multidimensional workflow net (MWF-net) includes multiple timing workflow nets (TWF-nets) and the organization and resource information. The processes of transaction instances form a queuing model in which the transaction instances act as customers and the resources act as servers. The key contribution of this paper is twofold. First, this paper presents a theoretical method to calculate the instances’ dwelling time probability density in a workflow where the activities are structured and predictable. Second, by this method the analysis of instances’ dwelling time distribution and satisfactory degree based on dwelling time can be achieved. The service time of an instance is specified by the firing delay of the corresponding transition (executing time of the corresponding activity). It is assumed that the service request (processing of a transaction instance) arrives with exponentially distributed inter-arrival times and the firing delay of a transition (executing time of the corresponding activity) follows exponential distribution. Then, the instances’ dwelling time probability density analysis in each activity and each control structure of a workflow model is performed. According to the above results a method is proposed for computing the instances’ dwelling time probability density in a workflow model. Finally an example is used to show that the proposed method can be effectively utilized in practice.