引用本文:张高生,朱进,谢宛青,奚宏生.一类离散时间非齐次马尔可夫跳跃系统最优控制[J].控制理论与应用,2016,33(1):128~132.[点击复制]
ZHANG Gao-sheng,ZHU Jin,XIE Wan-qing,XI Hong-sheng.Optimal control for a class of discrete-time nonhomogeneous Markovian jump linear systems[J].Control Theory and Technology,2016,33(1):128~132.[点击复制]
一类离散时间非齐次马尔可夫跳跃系统最优控制
Optimal control for a class of discrete-time nonhomogeneous Markovian jump linear systems
摘要点击 3474  全文点击 2662  投稿时间：2015-02-04  修订日期：2015-07-24
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DOI编号  10.7641/CTA.2016.50117
  2016,33(1):128-132
中文关键词  随机系统  非齐次马尔可夫链  最优控制  分离定理
英文关键词  stochastic systems  nonhomogeneous Markov chains  optimal control  separation principle
基金项目  国家自然科学基金项目(61374073), 中央高校基本科研业务费专项资金(WK2100000003), 安徽省自然科学基金项目(1308085QF107)资助.
作者单位E-mail
张高生 中国科学技术大学  
朱进* 中国科学技术大学 jinzhu@ustc.edu.cn 
谢宛青 中国科学技术大学  
奚宏生 中国科学技术大学  
中文摘要
      本文研究了一类离散时间非齐次马尔可夫跳跃线性系统的线型二次高斯(linear quadratic Gaussian, LQG) 问题, 其中系统模态转移概率矩阵随时间随机变化, 其变化特性由一高阶马尔可夫链描述. 对于该系统的LQG问题, 文中首先给出了线性最优滤波器, 得到最优状态估计; 其次, 验证分离定理成立, 并利用利用动态规划方法设计了系 统最优控制器; 最后, 数值仿真结果验证了所设计控制器的有效性.
英文摘要
      This paper concerns the linear quadratic Gaussian (LQG) problem for a class of discrete-time nonhomogeneous Markovian jump linear systems (MJLSs) in the presence of process and observation noises. In such nonhomogeneous MJLSs, the mode transition probability matrix (MTPM) varies randomly instead of being time-invariant. Assuming that the stochastic variation of MTPM is governed by a high level Markov chain, we propose an MJLS model with two-level Markov chains to describe the concerned characteristics. Firstly, a mode-MTPM based optimal filter is developed to estimate system states where the filter gain can be obtained from the coupled Riccati equations. Furthermore, we prove in details the validity of separation principle for such MJLSs. On this basis, we design the optimal output feedback controller by applying the dynamic programming method. Finally a numerical example is given to show the effectiveness of the developed theoretical results.