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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。
The stochastic Nash differential game for discrete-time Markov switching systems is discussed. By extending the single-player game to the game of two players, we obtain the equilibrium of stochastic Nash differential game for discrete-time Markov switching systems in finite time-domain and infinite-time domain, respectively, and prove the necessary and sufficient conditions for the existence of equilibrium solutions. The solution exists for the corresponding differential (algebraic) Riccati equation, and the explicit form of the optimal solution is given. Finally, the results are applied to stochastic mixed H 2 / H ∞ robust control problems in discrete-time linear Markov switching systems.