论文部分内容阅读
针对噪声依赖于状态的 It?型随机奇异系统，分别讨论有限时域和无限时域下的零和微分博弈问题。首先，基于线性二次最优控制，分别建立了有限时域和无限时域随机奇异系统零和微分博弈模型，在此基础上，通过配方法，得到了有限时域随机奇异系统零和微分博弈问题的均衡解等价于相应的耦合Riccati微分方程存在解，无限时域随机奇异系统零和微分博弈问题的均衡解等价于相应的耦合Riccati代数方程存在解，并给出了鞍点均衡策略，最后给出了数值算例。“,”In this paper, the problem of zero-sum games for stochastic singular systems governed by It?-type equation in finite-time horizon and infinite-time horizon are discussed respectively. Firstly, based on the LQ control, the model of zero-sum games in finite-time horizon and infinite-time horizon are constructed. Then, by the square completion technique, the existence of the strategies in finite-time horizon is presented by means of a set of cross-coupled Riccati differential equations, and the existence of the strategies in infinite-time horizon is presented by means of a set of cross-coupled Riccati algebraic equations. Then the saddle point equilibrium strategies are also given. At the end, a numerical example is given.