噪声依赖状态和控制的时滞非线性随机系统Nash微分博弈  

Nash Differential Games for Delayed Nonlinear Stochastic Systems with State-and Control-dependent Noise

作　　者：李洁茗 朱怀念[2] 

机构地区：[1]广东工业大学国际教育学院,广东广州511495 [2]广东工业大学经济与贸易学院,广东广州510520

出　　处：《广东工业大学学报》2018年第1期41-45,60,共6页Journal of Guangdong University of Technology

基　　金：国家自然科学基金资助项目(71571053);广东省自然科学基金资助项目(2015A030310218;2016A030313701);广东省教育厅普通高校特色创新项目(2015WTSCX014)

摘　　要：研究了一类噪声依赖于状态和控制的时滞非线性随机系统的2人Nash微分博弈问题,借助4个耦合的HamiltonJacobi方程组(HJEs)得到了Nash均衡策略存在的充分条件,即耦合HJEs如果存在解,Nash均衡策略就存在.同时给出了Nash均衡策略的显式表达.最后,通过一个数值算例验证了文中所得结论的有效性.The problem of two-person Nash differential games for delayed nonlinear stochastic systems with stateand control-dependent noise is discussed. A sufficient condition for the existence of the Nash equilibrium strategy is presented in terms of coupled Hamilton-Jacobi equations(HJEs). And meanwhile, the explicit expression of the equilibrium strategy is given. In the end, a numeric example is employed to show the effectiveness of the obtained results.

关 键 词：时滞非线性随机系统 微分博弈 NASH均衡 Hamilton-Jacobi方程组 

分 类 号：F224.32[经济管理—国民经济]