非自治的二人微分博弈  

Two-person Differential Games with Nonautonomous

作　　者：张芬[1] 王源昌[1] 雷丹[1] 

机构地区：[1]云南师范大学数学学院,云南昆明650500

出　　处：《云南师范大学学报（自然科学版）》2014年第6期8-13,共6页Journal of Yunnan Normal University:Natural Sciences Edition

基　　金：国家自然科学基金资助项目(71163046)

摘　　要：基于最优控制理论刻画二人微分博弈.首先,引进最优控制的状态方程和性能指标;其次,利用(DGP)τ定义微分博弈状态方程和性能指标,并用双极值原理得到最优控制对的显示表达式;然后,用拟黎卡提方程和非自治的二人微分博弈相结合,并且说明用双极值得到的是最优策略存在且唯一;最后,给出实例分析.In this study,the two-person differential games with nonautonomous was described based on the optimal control theory. First of all,the equation of state and the performance index were introduced; Secondly, the differential games problem was denoted by using （DGP）, and the representation of optimal control was obtained by using the maximum principle and minimum principle; Then, the so-called quasi-Riccati equation with the nonautonomous Two-Person differential was synthesized. Furthermore,we tested that using the maximum principle and minimum principle can prove that there exists a unique pair of optimal strategies. Finally,the example was analyzed.

关 键 词：最优控制 鞍点 最优策略 最大值原理 最小值原理 

分 类 号：O225[理学—运筹学与控制论] O232[理学—数学]