奇异随机Markov跳变系统的N人Nash博弈问题

Nash Games of Singular Stochastic Markov Jump Systems with N Decision Makers

分别研究了有限时间和无限时间情形下的一类奇异随机Markov跳变系统的N人微分博弈问题.利用配方法,得到了有限时间N人博弈的Nash均衡策略的微分Riccati方程,证明了Nash均衡策略的存在条件等价于微分Riccati方程存在解;无限时间内,N人博弈的Nash均衡策略的存在条件等价于代数Riccati方程存在解,并分别给出了均衡策略的显式表达及最优性能泛函值.最后,将所得的结果应用于现代鲁棒控制中的随机H_2/H_∞控制问题,得到了鲁棒控制策略的存在条件及显式表达.

A class of Nash differential games of continuous-time singular stochastic Markov jump systems of with multiple decision makers is investigated in this paper. Both the cases of finite-time horizon and infinite-time horizon are discussed, respectively. By utilizing the square completion technique, the existence conditions of Nash equilibrium is obtained by differential Riccati equations in finite-time horizon, and the existence conditions of Nash equilibrium is obtained by algebra Riccati equations in infinite-time horizon. Explicit expressions of equilibrium strategy and optimal performance functional are given. In the end, we use the obtained results to deal with the stochastic N2/H∞ control problem in the fields of modern robust control, and the existence condition of robust control strategies and explicit expression are obtained.