| NUMERICAL METHOD BASED ON HAMILTON SYSTEM AND SYMPLECTIC ALGORITHM TO DIFFERENTIAL GAMES |
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| 作者姓名： | 徐自祥 周德云 邓子辰 |
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| 作者单位： | School of Electron and Information Northwestern Polytechnical University Xi'an 710072，P. R. China，School of Electron and Information Northwestern Polytechnical University，Xi'an 710072，P. R. China，Department of Engineering Mechanics Northwestern Polytechnical University，Xi'an 710072，P. R. China |
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| 摘 要： | The resolution of differential games often concerns the difficult problem of two points border value (TPBV), then ascribe linear quadratic differential game to Hamilton system. To Hamilton system, the algorithm of symplectic geometry has the merits of being able to copy the dynamic structure of Hamilton system and keep the measure of phase plane. From the viewpoint of Hamilton system, the symplectic characters of linear quadratic differential game were probed; as a try, Symplectic-Runge-Kutta algorithm was presented for the resolution of infinite horizon linear quadratic differential game. An example of numerical calculation was given, and the result can illuminate the feasibility of this method. At the same time, it embodies the fine conservation characteristics of symplectic algorithm to system energy.
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| 关 键 词： | 数字方法 微分对策 汉密尔顿系统 偶对几何算法 线性二次方程 |
| 收稿时间： | 2004-11-23 |
| 修稿时间： | 2005-11-15 |
Numerical method based on Hamilton system and symplectic algorithm to differential games |
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| Zi-xiang Xu,De-yun Zhou,Zi-chen Deng.NUMERICAL METHOD BASED ON HAMILTON SYSTEM AND SYMPLECTIC ALGORITHM TO DIFFERENTIAL GAMES[J].Applied Mathematics and Mechanics(English Edition),2006,27(3):341-346. |
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| Authors: | Zi-xiang Xu De-yun Zhou Zi-chen Deng |
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| Institution: | 1. School of Electron and Information, Northwestern Polytechnical University,Xi'an 710072, P. R. China
2. Department of Engineering Mechanics, Northwestern Polytechnical University, Xi'an 710072, P. R. China |
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| Abstract: | The resolution of differential games often concerns the difficult problem of two points border value (TPBV), then ascribe linear quadratic differential game to Hamilton system. To Hamilton system, the algorithm of symplectic geometry has the merits of being able to copy the dynamic structure of Hamilton system and keep the measure of phase plane. From the viewpoint of Hamilton system, the symplectic characters of linear quadratic differential game were probed; as a try, Symplectic-Runge-Kutta algorithm was presented for the resolution of infinite horizon linear quadratic differential game. An example of numerical calculation was given, and the result can illuminate the feasibility of this method. At the same time, it embodies the fine conservation characteristics of symplectic algorithm to system energy. |
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| Keywords: | differential game Hamilton system algorithm of symplectic geometry linear quadratic |
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