三类带有泊松跳时滞非线性随机控制系统的稳定性

发布时间：2018-03-08 19:07

本文选题：非线性随机控制系统　切入点：泊松过程　出处：《哈尔滨工业大学》2017年硕士论文　论文类型：学位论文

【摘要】：近年来,基于伊藤型随机微分或随机差分方程建模的离散随机动力系统一直都倍受人们的广泛关注。现实中,很多随机现象和时间延迟都会不可避免的存在,而随机干扰和延迟的出现对系统的稳定性有很大的影响,因此,研究随机延迟动力系统的稳定性受到了越来越多学者的青睐。注意到,泊松过程能够很好的描述跳跃随机现象,于是,带有泊松跳的离散延迟非线性随机控制系统的稳定性分析是一项值得深入研究的课题。本文主要研究几类带有泊松跳的离散延迟非线性随机控制系统的稳定性。值得注意的是,为了缩小计算成本,本文给出了一种新的有效处理泊松过程的方法,即补偿法。文章具体研究内容如下:首先研究了带有泊松过程和离散时间延迟的非线性随机控制系统的稳定性。基于Lyapunov-Krasovskii泛函和线性矩阵不等式技巧,得出一些均方意义下的全局渐近稳定性准则。同时,给出了反馈控制矩阵的具体求解公式。数值算例验证了理论结果的有效性。其次,考虑到系统的历史会对现在的状态产生影响,引入了另一种时间延迟—分布延迟。给出了带有泊松过程和混合时间延迟离散非线性随机控制系统的均方意义下的全局渐近稳定性定理和求解反馈控制矩阵的公式。最后,由于随机扰动的多样性,在离散非线性随机系统带有泊松过程和混合延迟的基础上,加入了布朗运动。通过分析,证明了带有混合时间延迟、泊松过程和布朗运动两种随机扰动的离散非线性随机系统的可控性,并用数值模拟加以说明了理论的有效性。
[Abstract]:In recent years, discrete stochastic dynamical systems based on Ito stochastic differential equations or stochastic difference equations have attracted much attention. In reality, many stochastic phenomena and time delays will inevitably exist. But the emergence of stochastic disturbance and delay have great influence on the stability of the system. Therefore, the study of the stability of stochastic delay dynamical system has attracted more and more scholars. It is noted that the Poisson process can well describe the jump stochastic phenomenon. So, The stability analysis of discrete delay nonlinear stochastic control systems with Poisson jump is a subject worth further study. This paper mainly studies the stability of some discrete delay nonlinear stochastic control systems with Poisson jump. In order to reduce the computational cost, a new and effective method for dealing with Poisson process is presented in this paper. The main contents of this paper are as follows: firstly, the stability of nonlinear stochastic control systems with Poisson process and discrete time delay is studied. Based on Lyapunov-Krasovskii functional and linear matrix inequality (LMI) technique, the stability of nonlinear stochastic control system with Poisson process and discrete time delay is studied. Some global asymptotic stability criteria in the mean square sense are obtained. At the same time, the concrete solution formulas of the feedback control matrix are given. Numerical examples verify the validity of the theoretical results. Considering that the history of the system will have an impact on the current state, Another time-delay distributed delay is introduced. The global asymptotic stability theorem for discrete nonlinear stochastic control systems with Poisson process and mixed time delay in the sense of mean square and the formula for solving the feedback control matrix are given. Because of the diversity of stochastic disturbances, the Brownian motion is added to the discrete nonlinear stochastic system with Poisson process and mixed delay. The controllability of discrete nonlinear stochastic systems with two stochastic perturbations of Poisson process and Brownian motion is demonstrated by numerical simulation.
【学位授予单位】：哈尔滨工业大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O231

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