摘要
针对噪声同时依赖于状态与控制的Ito型离散Markov切换系统的随机零和博弈问题,分别讨论了其在有限时域和无限时域情形的鞍点均衡策略.利用配方法,得到了随机零和博弈问题存在解的充分必要条件等价于相应的耦合Riccati差分(代数)方程存在解,并给出了最优解的显式形式.然后把所得的结果应用于相应的H_∞o控制问题,得到了H_∞控制策略的Riccati方程,最后给出了数值算例.
The linear quadratic stochastic zero-sum games for discrete-time Markov jump systems with state and control-dependent noise are discussed in this paper. By the square completion technique, it is shown that the necessary and sufficient conditions for the existence of stochastic zero-sum games is equivalent to the solvability of the associated cross-coupled Riccati algebraic equations. Moreover, the explicit expressions of the optimal strategies are constructed, and the results are applied to H∞ control problem for discrete-time Markov jump systems. Moreover, an illustrative example is also proposed.
出处
《系统科学与数学》
CSCD
北大核心
2016年第12期2200-2210,共11页
Journal of Systems Science and Mathematical Sciences
基金
国家自然科学基金(71171061)
广东省自然科学基金(S2011010004970)
广东省自然科学基金(2014A030310366
2015A030310218)资助课题
中国博士后科学基金(2014M552177)
