项目名称: 随机混合时滞系统的稳定性分析与脉冲控制器设计
项目编号: No.61304068
项目类型: 青年科学基金项目
立项/批准年度: 2014
项目学科: 自动化技术、计算机技术
项目作者: 李燕
作者单位: 华中农业大学
项目金额: 23万元
中文摘要: 本项目拟对由随机时滞系统、Markov跳变系统和脉冲瞬时突变系统相结合的随机混合时滞系统进行研究。主要对随机混合时滞系统的随机输入状态稳定性和随机积分输入状态稳定性进行分析,综合考虑时滞性、Markov跳变性、脉冲突变性,计算合理的时滞区间,设计脉冲控制器使系统稳定。具体内容:(1)刻画随机混合时滞系统的随机输入状态稳定和随机积分输入状态稳定的定义,比较这两个定义的强弱,寻找实例验证定义的合理性;(2)构造带有脉冲系统的随机混合时滞系统Skorohod函数空间,建立相关的渐近性质,利用相应的Razumikhin技巧或Lyapunov-Krasovskii泛函方法,论证系统的随机输入状态稳定和随机积分输入状态稳定;(3)考虑不同子系统,寻找在比较合理的时滞区间,利用Markov控制率,设计最优脉冲控制器,仿真模拟,应用到实际系统中。本项目的研究对随机系统的综合与分析具有重要的理论意义和应用。
中文关键词: 随机混合系统;稳定性;Markov跳跃;脉冲控制器设计;时滞系统
英文摘要: This research project aims to explore stochastic hybrid delay systems combinated by stochastic delay systems, Markov jump systems and impulsive transient mutation systems. The stochastic input-to-state stability and stochastic integral input-to-state stability are studied. The reasonable intervals of delay are computed, and the impulsive controllers are designed by using the delay, Markov jump, and impulsive transient mutation. Specifically, (1)Define the stochastic input-to-state stability and stochastic integral input-to-state stability,compare the two definitions, give the examples to verify the rationality of the defintions; (2) Structure the Skorohod function space of stochastic hybrid delay systems with impulsive, establish the asymptotic properties, use the Razumikhin technique or Lyapunov - Krasovskii functional methods to prove the stochastic input-to-state stability and stochastic integral input-to-state stability; (3)To different systems, compute the more reasonable delay interval, design the optimal controllers by using Markovian control law, and simulate, apply to the actual system. The research of this project is important in theory and applications on the synthesis and analysis of the stochastic systems.
英文关键词: stochastic hybrid systems;stability;markov jump;impulsive controller design;delay systems