离散Markov切换系统的随机Nash博弈及H_2/H_∞控制  

Stochastic Nash Games and H_2/H_∞ Control for Discrete-time Markov Jump Systems

作　　者：周海英[1] 张成科[2] 朱怀念[2] 

机构地区：[1]广州航海学院港口与航运管理系,广州510725 [2]广东工业大学经济与贸易学院,广州510520

出　　处：《控制工程》2016年第6期828-833,共6页Control Engineering of China

基　　金：国家自然科学基金(71171061);广东省自然科学基金(S2011010004970);广东省哲学社会科学"十二五"规划(GD14YGL01)

摘　　要：讨论离散时间Markov切换系统的随机Nash微分博弈问题。通过把单人博弈推广到两人博弈的方法,分别得到了有限时域和无限时域下的离散时间Markov切换系统的随机Nash微分博弈问题的均衡解,证明了均衡解存在的充分必要条件等价于相应的差分(代数)Riccati方程存在解,并给出了最优解的显式形式。最后,将所得结果应用于分析离散时间线性Markov切换系统的随机混合H_2/H_∞鲁棒控制问题。In this paper, linear quadratic stochastic Nash differential games for discrete-time Markov jump systems in finite time horizon and infinite time horizon are studied respectively. By utilizing the results of one-person differential game for Markov jump linear systems, the existence conditions of the two-person stochastic differential games are equivalent to the solvability of the associated algebraic Riccati equations. Moreover, the explicit expressions of the optimal strategies are constructed. The results are also applied to the mixed H_2/H_∞ robust control problem for stochastic discrete-time Markov jump systems.

关 键 词：离散Markov切换系统 随机微分博弈 H2/H∞鲁棒控制 RICCATI方程 

分 类 号：TP13[自动化与计算机技术—控制理论与控制工程]