A numerical solution of open-loop Nash equilibrium in nonlinear differential games based on Chebyshev pseudospectral method

作者：Nikooeinejad Z^*; Delavarkhalafi A; Heydari M

来源：Journal of Computational and Applied Mathematics, 2016, 300: 369-384.

DOI：10.1016/j.cam.2016.01.019

• Nonzero-sum differential games
• Open-loop Nash equilibria
• Boundary value problems
• Chebyshev pseudospectral method

In general, the applications of differential games for solving practical problems have been limited, because all calculations had to be done analytically. In this investigation, a simple and efficient numerical method for solving nonlinear nonzero-sum differential games with finite- and infinite-time horizon is presented. In both cases, derivation of open-loop Nash equilibria solutions usually leads to solving nonlinear boundary value problems for a system of ODEs. The proposed numerical method is based on a combination of minimum principle of Pontryagin and expanding the required approximate solutions as the elements of Chebyshev polynomials. Applying Chebyshev pseudospectral method, two-point boundary value problems in differential games are reduced to the solution of a system of algebraic equations. Finally, several examples are given to demonstrate the accuracy and efficiency of the proposed method and a comparison is made with the results obtained by fourth order Runge Kutta method.

• 出版日期2016-7