切换-Markov跳变随机混杂系统控制研究

项目名称： 切换-Markov跳变随机混杂系统控制研究

项目编号： No.61473107

项目类型： 面上项目

立项/批准年度： 2015

项目学科： 自动化技术、计算机技术

项目作者： 陈云

作者单位： 杭州电子科技大学

项目金额： 80万元

中文摘要： 切换系统和马尔可夫（Markov）跳变系统是两类重要的混杂系统，它们能有效描述许多实际对象，其研究有重要理论和应用价值。具有监督控制的马尔可夫跳变系统等复杂被控对象同时存在确定性切换和随机跳变，这类切换-马尔可夫跳变系统成为近期研究的热点。考虑实际对象普遍存在随机扰动，本项目将进行切换-马尔可夫跳变随机混杂系统的控制研究。本项目有重要理论意义，在许多行业应用前景广泛。 主要研究内容：1）利用构造非卷积多Lyapunov函数和鞅分析等方法，研究切换随机系统的分析与控制问题，使平均驻留时间不依赖于给定参数；2）基于马尔可夫过程和布朗运动样本路径的大偏差原理，分别建立切换-马尔可夫跳变系统和切换-马尔可夫跳变随机混杂系统的控制方法；3）通过构造随机辅助向量系统和相应的多层次自适应反推的设计方法，解决多变量非线性随机系统和多变量切换-马尔可夫跳变随机混杂系统的自适应控制问题；4）仿真和实验验证。

中文关键词： 确定性切换；Markov跳变；非卷积多Lyapunov函数；大偏差原理；多层次自适应反推

英文摘要： Switched systems and Markov jump systems, two important categories of hybrid systems, can be used efficiently to described many practical plants, so the studies of these hybrid systems are both theoretically and practically valuable. Some complex controlled plants, for example, Markov jump systems with controllers selected by supervisors, are subject to both deterministic switching and stochastic jump, and these hybrid systems have received lots of research interests recently. Due to the universality of stochastic perturbations in real-world systems, this project will investigate the issue of control for stochastic hybrid systems with deterministic switchings and Markov jump, i.e., switching-Markov jump stochastic hybrid systems. This project has important theoretical significances and extensive applications in many fields. The main contents of this project include: 1) by the construction of non-convolution type multiple Lyapunov functions, martingale analysis and some other techniquess, the analysis and control problems of switched stochastic systems are considered with the average dwell time independent on any given parameters. 2) Based on large deviations principles (LDPs) of Markov processes and Brownian motion sample paths, control methods for switching-Markov jump systems and switching-Markov jump stochastic hybrid systems are established, respectively. 3) Stochastic auxiliary vector systems and the corresponding multilevel adaptive backstepping approach are presented to solve the issues of adaptive control for multivariable nonlinear stochastic systems and multivariable switching-Markov jump stochastic hybrid systems. 4) The methods and main results of this project are verified by numerical simulations and experiments.

英文关键词： deterministic switching;Markov jump;non-convolution type multiple Lyapunov function;large deviations principle;multilevel adaptive backstepping