广东工业大学学报2024，Vol.41Issue(2)：129-138,10.DOI:10.12052/gdutxb.230010
转移概率部分未知的离散时间Markov跳变系统Nash微分博弈
Nash Differential Game for Discrete-time Markov Jump System with Partially Unknown Transition Probabilities
摘要
Abstract
It is noted that transition probability matrix elements cannot be fully known.How to study Nash differential game for discrete-time Markov jump system(MJS)under the condition of unknown transition probability is one of the problems to be solved.This problem can provide theoretical support for the application of Nash differential game theory in Markov jump systems with partial unknown transition probability to management problems.Based on it,the case of one-player game,which is called the ε-suboptimal control problem,is firstly studied.By using the free-connection weighting matrix and"complete square"method,the sufficient conditions for the existence of the ε-suboptimal cntrol strategy are obtained,and an explicit expression of the upper bound of the cost function is given.Then,the conditions for the existence of ε-suboptimal Nash equilibrium strategy are equivalent to solving the optimization problem,which satisfied the bilinear matrix inequalities(BMIs)and matrix inequalities.The heuristic algorithm is used to solve the optimization problem to obtain the ε-suboptimal Nash equilibrium strategies.Finally,the numerical examples are provided to demonstrate the validity of the main conclusions.关键词
离散时间Markov跳变系统/ε-次优控制/ε-次优Nash均衡Key words
discrete time Markov jump system/ε-suboptimal control/ε-suboptimal Nash equilibrium分类
管理科学引用本文复制引用
张成科,徐萌,杨璐..转移概率部分未知的离散时间Markov跳变系统Nash微分博弈[J].广东工业大学学报,2024,41(2):129-138,10.基金项目
国家自然科学基金资助项目(71571053) （71571053）
国家社会科学基金后期资助暨优秀博士论文项目(21FJYB025) （21FJYB025）
广东省基础与应用基础研究基金资助项目(2023A1515012335) （2023A1515012335）
