Symplectic For Many-Person Nonlinear Differential Games

In 1956,Dr.Issacs published the first book about differential ga-mes,which was named Differential Games and marked the official b-irth of differential games. It attracted many researchers from all th-e world, however,It's all about the linear quadratic for a long time,e-specially two-person linear quadratic differential games. Due to thedifficulty in theory,few did study nonlinear differential games,but weknow,practical problems often are nonlinear,so,research on numericalmethods and algorithm of non-linear differential game gradually bec-omes a hot direction.For two-person nonlinear quadratic differential games,we can us-e H-J-B.but many-person nonlinear differential games,we need find t-he new method for the complexity. Chapter I,II of this article is about transforming nonlinear diff-erential games into a linear one, then with the help of T-S fuzzy model,keeping the global non-linear nature,and the Hamilton system,we can solve it symplectic algorithm which keeps the overall flow characteristics and system conservation laws. Chapter III and IV areon two-person nonlinear and many-person nonlinear differential gam-es,and confirmed by examples: It's possible to solve differential ga- mes by symplectic algorithm ,and the numerical results are satisfactory.Chapter IV generalizes the case of two-person linear differentialgames,proves that many-person linear quadratic differential game ca-n also be attributed to the hamilton system,and it will be a theoreti-cal foundation on solving differential games.Main innovation:1. Propose how to make sure the membership function of T-S fuzzy model and give out the general solution;2. Prove many-person linear quadratic differential games is a h-amilton system, and symplectic algorithm can solve it.3. Examples on nonlinear differential games: T-S fuzzy model,symplectic difference method,and the results show this meth-od feasible.This paper is mainly about differential games whose payment f-unction is quadratic,for non-quadratic differential game, we can getby the approximation method.Chapter V of this article, according to the rule"Graduate gradu-ation requirements Department of Mathematics Shanghai Jiaotong University ",is a general report based on thinking, refined, innovativ-e after reading, understanding a lot of technology literature. (Mainl-y about the classical trajectories of molecules, Differential Games, vibration systems and symplectic Runge-Kutta methods, multi-sympl-ectic algorithms.)...