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		Xiaohong NIAN,Zhisheng DUAN,Wenyan TANG.[en_title][J].Control Theory and Technology,2006,4(3):239~244.[Copy]

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XiaohongNIAN,ZhishengDUAN,WenyanTANG
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Received:June 14, 2004Revised:March 21, 2006

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Analytical solution for a class of linear quadratic open-loop Nash game with multiple players

Xiaohong NIAN, Zhisheng DUAN, Wenyan TANG

(School of Information Science & Engineering, Central South University, Changsha Hunan 410075, China; Center for Systems and Control, Department of Mechanics and Engineering Science, Peking University, Beijing 100871, China)

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.

Key words: Linear quadratic games Open-loop Nash equilibrium Riccati-type differential equations