带Poisson跳的线性二次随机微分博弈及其在鲁棒控制中的应用  

Linear Quadratic Stochastic Differential Games with Poisson Jumps and Their Application to Robust Control

作　　者：张成科[1] 曹铭[2] 朱怀念[1] 朱莹[2] 程硕[2] 

机构地区：[1]广东工业大学经济与贸易学院,广东广州510520 [2]广东工业大学管理学院,广东广州510520

出　　处：《信息与控制》2016年第3期257-265,共9页Information and Control

基　　金：国家自然科学基金资助项目(71171061;71571053);中国博士后科学基金资助项目(2014M552177);广东省自然科学基金项目(2014A030310366;2015A030310218);广东工业大学校青年基金资助项目(14QND002)

摘　　要：研究了一类带Poisson跳扩散过程的线性二次随机微分博弈,包括非零和博弈的Nash均衡策略与零和博弈的鞍点均衡策略问题.利用微分博弈的最大值原理,得到Nash均衡策略的存在条件等价于两个交叉耦合的矩阵Riccati方程存在解,鞍点均衡策略的存在条件等价于一个矩阵Riccati方程存在解的结论,并给出了均衡策略的显式表达及最优性能泛函值.最后,将所得结果应用于现代鲁棒控制中的随机H_2/H_∞控制与随机H_∞控制问题,得到了鲁棒控制策略的存在条件及显式表达,并验证所得结果在金融市场投资组合优化问题中的应用.In this paper,we investigate a class of linear quadratic stochastic differential games with a Poisson jumps diffusion process,including the Nash equilibrium strategies of a nonzero sum game and the saddle point equilibrium strategies of a zero sum game. Utilizing the maximum principle for differential games,we determine that the existence conditions of the Nash equilibrium strategies are equivalent to the solution for two cross-coupled matrix Riccati equations,and that the existence conditions of the saddle point equilibrium strategies are equivalent to the solution for a matrix Riccati equation. We also provide explicit expressions for the equilibrium strategy and the optimal performance functional value. Finally,we apply the obtained results to problems dealing with stochastic H2/ H∞control and stochastic H∞control in the fields of modern robust control theory,and obtain the existence conditions of robust control strategies and their explicit expressions. Moreover,we verify the performance of these results in a financial market portfolio optimisation problem.

关 键 词：随机微分博弈 矩阵Riccati方程 随机H2/H∞控制 

分 类 号：F224.32[经济管理—国民经济]