带有无限马尔可夫跳跃的离散系统LQ纳什博弈

LQ Nash Games for Discrete Systems with Infinite Markov Jumps

研究具有无限马尔可夫跳跃和(x,u,v)-独立噪声的随机微分方程(SDEs)的无限时域线性二次(LQ)纳什博弈问题。基于矩阵伪逆性质,算子理论,状态稳定性性质,给出不定LQ控制的可达性与ICGAREs解的存在性之间的等价条件。在此基础上,在EMSS-C和强可检测性条件下,确定了无限马尔可夫跳跃系统的无限时域纳什对策。

In this paper, we consider infinite horizon linear-quadratic (LQ) Nash games for stochastic differen-tial equations (SDEs) with infinite Markovian jumps and (x,u,v) -dependent noise. Based on the pseudo-inverse property of matrix, operator theory and state stability property, the equivalent conditions between the reachability of indefinite LQ control and the existence of ICGAREs solution are given. On this basis, the infinite-domain Nash games for infinite Markov jump systems are de-termined under the conditions of EMSS-C and strong detectability.