基于T-S模糊建模思想的多人非合作微分对策

N-player Noncooporative Differential Games Based on the Thought of T-S Fuzzy Modeling

多人微分对策的研究是微分对策研究领域的难点。如果微分对策的状态方程和支付函数是非线性的,研究的方法有双边极值原理和变分法,那么就不可避免的要求解Hamilton-Jacobi偏微分方程组,这样的求解是比较困难的。针对非线性系统的多人微分对策,利用T-S模糊思想方法将非线性系统转化成若干个线性子系统,并对多个局中人进行分组,从而建立了多人非合作微分对策模型,最后举出一个4人非合作的实例进行仿真试验,效果说明了解决问题方法的可行性。

N - player differential game has always been a difficult point in the research field of differential games. If the state equations and payoff fucntion of differential games are nonlinear, the research methods are Max - Min principle and Variational method, which anavoidably need to solve the Hamilton - Jacobi partial differential equations, and that is very difficult. In view of the problem of the N - player differential games of nonlinear system, based on the thought of T - S fuzzy modeling, the nonlinear system has been translated into many linear subsystems. Then, a model of N - player noncooporative differential games has been established. A simulation for 4 - player noncooporative Differential games has been made and its results has illuminated the feasibility of the scheme.