| Analytical solution for a class of linear quadratic open-loop Nash game with multiple players |
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| 作者姓名： | Xiaohong NIAN Zhisheng DUAN Wenyan TANG |
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| 作者单位： | [1]School of Information Science ＆ Engineering, Central South University, Changsha Hunan 410075, China [2]Center for Systems and Control, Department of Mechanics and Engineering Science, Peking University, Beijing 100871, China |
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| 基金项目： | This work was supported by the National Natural Science Foundation of China（No.60474029） and China Postdoctoral Science Foundation （No.2005038558）.Acknowledgements The authors would like to thank Professor Huang Lin for bringing this topic to our attention, and we are also grateful to anonymous referees for their valuable comments and helpful suggestion to improve this paper. |
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| 摘 要： | In this paper, the Nash equilibria for differential games with multiple players is studied. A method for solving the Riccati-type matrix differential equations for open-loop Nash strategy in linear quadratic game with multiple players is presented and analytical solution is given for a type of differential games in which the system matrix can be diagonalizable. As the special cases, the Nash equilibria for some type of differential games with particular structure is studied also, and some results in previous literatures are extended. Finally, a numerical example is given to illustrate the effectiveness of the solution procedure.
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| 关 键 词： | 解析解 线性二次开环 游戏 微分方程 |
| 收稿时间： | 2004-06-14 |
| 修稿时间： | 2006-03-21 |
Analytical solution for a class of linear quadratic open-loop Nash game with multiple players |
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| Xiaohong NIAN,Zhisheng DUAN,Wenyan TANG.Analytical solution for a class of linear quadratic open-loop Nash game with multiple players[J].Journal of Control Theory and Applications,2006,4(3):239-244. |
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| Authors: | Xiaohong NIAN Zhisheng DUAN Wenyan TANG |
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| Affiliation: | 1. School of Information Science & Engineering,Central South University,Changsha Hunan 410075,China
2. Center for Systems and Control,Department of Mechanics and Engineering Science,Peking University,Beijing 100871,China |
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| Abstract: | In this paper, the Nash equilibria for differential games with multiple players is studied. A method for solving the Riccati-type matrix differential equations for open-loop Nash strategy in linear quadratic game with multiple players is presented and analytical solution is given for a type of differential games in which the system matrix can be diagonalizable. As the special cases, the Nash equilibria for some type of differential games with particular structure is studied also, and some results in previous literatures are extended. Finally, a numerical example is given to illustrate the effectiveness of the solution procedure. |
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| Keywords: | Linear quadratic games Open-loop Nash equilibrium Riccati-type differential equations |
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