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

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.

This paper concerns the linear quadratic Gaussian （LQG） problem for a class of discrete-time nonhomoge- neous 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 es- timate 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.