基于驻留时间均方稳定的“切换-跳变”系统控制

项目名称： 基于驻留时间均方稳定的“切换-跳变”系统控制

项目编号： No.61203126

项目类型： 青年科学基金项目

立项/批准年度： 2013

项目学科： 自动化学科

项目作者： 闻继伟

作者单位： 江南大学

项目金额： 23万元

中文摘要： Markov跳变系统是混杂系统理论领域中的独特分支，其直观的动力学行为本质上由各工作模态之间的跳变转移概率决定。本项目将控制作用和跳变频率对转移概率的影响，归结到"切换-跳变"系统(S-MJS)模型的统一框架下处理，即以具有随机跳变特性的Markov跳变系统为核心，结合具有确定切换特点的切换信号，形成"监督器-备用控制器-子系统-工作模态"的递阶式控制系统模型。基于驻留时间均方稳定特性，项目主要研究内容包括：(1)利用驻留时间法或多Lyapunov函数方法研究S-MJS的稳定性分析与综合问题；(2)合理划分子系统激励时间，构造分段连续的Lyapunov函数，设计异步切换控制器；(3)构建S-MJS的不变集空间，设计约束切换控制器；(4)针对S-MJS的整体性能设计滚动时域控制器，兼顾性能优化，初始可行域和在线计算量。项目研究不仅包含丰富的理论内涵同时也具有显著的工程应用价值。

中文关键词： 切换-跳变系统；驻留时间均方稳定；异步切换；有限时间控制；平均驻留时间

英文摘要： As a special class of hybrid system, Markov jump system (MJS) has received much attention in recent years. As a significant fact, transition probabilities (TPs) of Markov process determine the system evolution to a great degree. In terms of engineering application, the TPs are limited by the control move and jump frequency, where the latter is closely associated with dwell time constraints. In this project, we are interested in considering both the controller switching and the jump frequency, which impact on the TPs. The research is attracted under a hybrid system model, which is referred to as switching MJS (S-MJS). The overall system is described by the combination of a finite number of linear subsystems, indexed by both the stochastic jumping signal, generated by nature, and the deterministic switching signal, selected by the supervisor. A hierarchical system model can be briefly boiled down to "supervisor, optional controller, subsystem, operation modes". Based on the mean square stability, the main research work can be summarized as follows. (1) Stability analysis and synthesis for S-MJS will be investigated by employing dwell time method or multiple-Lyapunov functional method. (2) The asynchronous switching controller design method will be studied by properly assigning a Lyapunov function, which varies pie

英文关键词： Switching-jump systems；Mean square stability with dwell time；Asynchronous switching；Finite-time control；Average dwell time