Markov跳跃系统的随机Stackelberg博弈及其应用  

The Stochastic Stackelberg Games for Markov Jump Systems and Its Application

作　　者：周海英 张成科[2] 朱怀念[2] 宾宁 ZHOU Hai-ying;ZHANG Cheng-ke;ZHU Huai-nian;BIN Ning(Department of Port and Sipping Management, Guangzhou Maritime College, Guangzhou 510725, China;School of Economics ＆ Commence, Guangdong University of Technology, Guangzhou 510520, China)

机构地区：[1]广州航海学院港口与航运管理学院,广州510725 [2]广东工业大学经济与贸易学院,广州510520

出　　处：《控制工程》2018年第6期1114-1121,共8页Control Engineering of China

基　　金：国家自然科学基金项目(71171061);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);广州航海学院创新创强项目(2017E12,2017C09,2017JI10)

摘　　要：针对噪声同时依赖状态与控制的离散Markov跳跃线性系统,应用配方法,讨论其在有限时间和无限时间情形下的随机Stackelberg博弈问题。首先给出了问题,应用配方法,分别得到了有限时间和无限时间情形下的离散Markov跳跃线性系统的随机Stackelberg策略,其策略存在的充分条件等价于相应的代数Riccati方程存在解,并给出了最优解的显式形式,然后根据博弈理论应用于鲁棒控制的思想,将所得结果应用于相应的H2/H∞控制问题,最后给出了数值算例。In this paper, linear quadratic stochastic Stackelberg games for Markov jump linear systems of discrete-time with state and control-dependent noise are studied. Firstly, the problem is formulated, then by using the square completion technique, the existence condition of finite time horizon and infinite time horizon Stackelberg strategies is equivalent to the solvability of the associated algebraic Riccati equations. Moreover, the explicit expressions of the optimal strategies are constructed. And then, based on the idea of the game theory applying to the robust control problem, the results are applied to the corresponding H2/H∞ control problem. In the end, the numerical simulation is also given.

关 键 词：随机线性Markov切换系统 Stackelberg策略 RICCATI方程 H2/H∞控制 

分 类 号：F224.32[经济管理—国民经济]