| 非自治的二人微分博弈 |
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| 引用本文： | 张芬,王源昌,雷丹.非自治的二人微分博弈[J].云南师范大学学报(自然科学版),2014(6):8-13. |
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| 作者姓名： | 张芬 王源昌 雷丹 |
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| 作者单位： | 云南师范大学 数学学院,云南 昆明,650500 |
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| 基金项目： | 国家自然科学基金资助项目 |
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| 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.
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| 关 键 词： | 最优控制 鞍点 最优策略 最大值原理 最小值原理 |
Two-person Differential Games with Nonautonomous |
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| ZHANG Fen,WANG Yuan-chang,LEI Dan.Two-person Differential Games with Nonautonomous[J].Journal of Yunnan Normal University (Natural Sciences Edition),2014(6):8-13. |
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| Authors: | ZHANG Fen WANG Yuan-chang LEI Dan |
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| Institution: | ZHANG Fen;WANG Yuan-chang;LEI Dan;School of Mathematics,Yunnan Normal University; |
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| Abstract: | 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. |
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| Keywords: | Optimal control Saddle point Optimal strategies Maximum principle Minimum principle |
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