转移概率一般有界的离散Markov跳变系统ε-次优Nash博弈问题  

ε-Suboptimal Nash Game of Discrete-Time Markov Jump Systems with Generally Bounded Transition Probabilities

作　　者：徐萌 张成科[2] 杨璐 曹铭 XU Meng;ZHANG Chengke;YANG Lu;CAO Ming(School of Management,Guangdong University of Technology,Guangzhou 510520;School of Economics Commence,Guangdong University of Technology,Guangzhou 510520;Management College,Guangdong Polytechnic Normal University,Guangzhou 510450;School of Economics&Trade,Guangdong University of Finance,Guangzhou 510521)

机构地区：[1]广东工业大学管理学院,广州510520 [2]广东工业大学经济与贸易学院,广州510520 [3]广东技术师范大学管理学院,广州510450 [4]广东金融学院经济贸易学院,广州510521

出　　处：《系统科学与数学》2024年第9期2620-2638,共19页Journal of Systems Science and Mathematical Sciences

基　　金：国家自然科学基金项目(7157053);国家社科基金资助项目(21FGYB205);广东基础及应用基础研究基金(2023A1515012335)资助课题。

摘　　要：文章研究了转移概率一般有界的离散时间Markov跳变系统的Nash微分博弈问题.引入自由权连接矩阵分离未知转移概率信息,结合配方法,得到了单人博弈的ε-次优控制策略的线性矩阵不等式和显式表达.证明了ε-次优控制策略存在的充分条件等价于求解满足一组线性矩阵不等式的优化问题.随后推导出双人和多人ε-次优的Nash均衡策略存在的充分条件等价于求解满足一组双线性矩阵不等式和线性矩阵不等式的最优化问题,并给出了启发式算法以求解.最后,通过经济系统仿真实例,证明了研究结果的有效性和实用性.This paper investigates the differential game problem for discrete-time Markov jump systems with generally bounded transition probabilities.By using the method of free-connection weighting matrix,the existence conditions of control strategy and the expression of the upper bound of performance index are proposed.It is proved that sufficient conditions for the existence ofε-suboptimal control strategy is equivalent to solving a set of optimization problems satisfying a set of linear matrix inequalities.Subsequently,it is deduced that the sufficient conditions for the existence of two-person and multi-person Nash equilibrium strategies are equivalent to solving optimization problem satisfying a set of bilinear matrix inequalities and linear matrix inequalities.A heuristic algorithm is given to solve them.Finally,the validity and practicability of the research results are proved by an example of economic system simulation.

关 键 词：转移概率 ε-次优Nash博弈 离散Markov跳变系统 自由连接权矩阵 

分 类 号：O231[理学—运筹学与控制论] O225[理学—数学]