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Hai-Jun Peng [1] and Sheng Zhang [1] and Zhi-Gang Wu [2] and Biao-Song Chen [1]

Academic Editor: Bozidar Sarler

, 1, , Department of Engineering Mechanics, , State Key Laboratory of Structural Analysis of Industrial Equipment, , Dalian University of Technology, , Dalian 116024, , China, , dlut.edu.cn,

, 2, , School of Aeronautics and Astronautics, , State Key Laboratory of Structural Analysis of Industrial Equipment, , Dalian University of Technology, , Dalian 116024, , China, , dlut.edu.cn,

This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

1. Introduction

The research for the differential game is derived from the military field, such as the pursuit evasion problem, the spacecraft interception problem, and the cooperative or noncooperative problem. The emergence of the Isaacs’s monograph [1] gives birth to the differential games. Particularly, the differential game has been introduced into the economic field by Nash [2], and the equilibrium solution of the LQ differential game had been named by Nash-equilibrium solution. So far, many works for the LQ differential games have been done by researchers.

The qualitative analysis about the LQ differential game, that is, the existence, stability of solutions, has been reported in many references. Reference [3] gives the series Nash solution of two-person nonzero-sum LQ differential game. Reference [4] discusses the Nash-equilibrium point and the existence, uniqueness of the algebraic Riccati equation for the closed LQ differential game. Reference [5] proposes the global existence of solutions to coupled Riccati differential equation (CRDE) in closed-loop Nash games. In contrast to the qualitative analysis, the numerical method for solving the LQ differential game problem to obtain the high performance solutions is still a challenging problem. Reference [6] founds that a special type of LQ differential game problem has the character of Hamiltonian system and applies the symplectic Runge-Kutta algorithm for solving this differential game problem. Reference [7] employs the Magnus integrators for solving N -player LQ differential games, and the CRDE which is reformulated as a linear ordinary equation is solved by Magnus integrators.

From the above discussions, the key for solving LQ differential game is to solve the CRDE. Only a few problems can obtain...

                     

   

      

   

       

               

               

 

       

   

       

       

   

 

 

 

     

     

   

           

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