离散广义随机Markov跳变系统零和博弈及应用

Zero-sum games of discrete-time stochastic singular markov jump systems

针对离散广义随机Markov跳变系统零和博弈问题,讨论了其在有限时间情形和无限时间情形下鞍点均衡策略。通过配方法,分别得到了有限时间和无限时间内,离散广义随机Markov跳变系统零和博弈问题均衡策略存在等价于相应的耦合Riccati差分(代数)方程存在解,并给出了最优解的显式表达式及最优值函数。然后根据现有研究,把所得结果应用于现代鲁棒控制中的随机H∞控制问题,得到了H∞控制策略存在的条件。

The linear quadratic stochastic zero-sum games for discrete-time singular Markov jump systems in finite time and infinite time are discussed respectively in this paper.By using the square completion technique,the conditions for the existence of stochastic zero-sum games are shown to be equivalent to the solvability of the associated cross-coupled Riccati algebraic equations.Moreover,the explicit expressions of the equivalent strategies and the optimal function are given.Furthermore,the obtained results are applied to the H∞control problem of discrete-time stochastic Singular Markov jump systems.The existence conditions of the stochastic H2/H∞control strategies and explicit expressions are given.