离散奇异随机系统的N人Nash博弈  

Nash Games of Discrete-time Stochastic Singular Systems with N Decision Makers

作　　者：周海英 ZHOU Hai-ying(School of Port and Sipping Management,Guangzhou Maritime University,Guangzhou Guangdong ,510725,China)

机构地区：[1]广州航海学院港口与航运管理学院

出　　处：《广州航海学院学报》2019年第2期52-56,共5页Journal of Guangzhou Maritime University

基　　金：广东省自然科学基金项目(2015A030310218);广州市哲学社会科学发展“十三五”规划课题(2017GZQN12);广东省本科高校创新创业教育改革研究项目(2018A063417);广州航海学院创新强校项目(2018WTSCX117)

摘　　要：针对It?型离散奇异随机系统的N人线性二次Nash博弈问题,讨论了其在有限时域情形和无限时域情形下的Nash均衡策略.利用配方法,分别得到有限时域和无限时域内,离散奇异随机系统二次线性N人Nash均衡策略存在的条件是相应耦合Riccati差分(代数)方程组存在解.并给出了最优解的显式表达式及最优值函数.借鉴前人研究成果,将所得最优策略应用于随机H2/H∞混合鲁棒控制问题,得到了随机H2/H∞混合鲁棒控制策略.The linear quadratic Nash games with N decision makers for discrete-time stochastic singular systems are discussed in this paper in finite time horizon and infinite time horizon respectively. By the square completion technique,it is shown that sufficient conditions for the existence of stochastic Nash games is equivalent to the solvability of the associated cross-coupled Riccati differential equations in finite time horizon,while the sufficient conditions for the existence of stochastic Nash games is equivalent to the solvability of the associated cross-coupled Riccati algebraic equations in infinite time horizon. Moreover,the explicit expressions of the optimal strategies are constructed,and the results are applied to H2 / H∞ control problem for discrete-time stochastic singular systems.

关 键 词：离散奇异随机系统 NASH 博弈 H2/H∞控制 RICCATI 方程 

分 类 号：F224.32[经济管理—国民经济]