基于Hamilton体系和辛算法的微分对策数值法

Numerical Method Based on Hamilton System and Symplectic Algorithm to Differential Games

微分对策求解往往涉及到困难的两点边值问题(TPBV),将线性二次型微分对策问题归结于Hamilton体系.对Hamilton系统,辛几何算法具有能复制Hamilton系统的动态结构并保持相平面上的测度的优点.从Hamilton系统角度,探讨了线性二次型微分对策系统的辛性质;作为尝试,对无限期间线性二次型微分对策的计算引入Symplectic_Runge_Kutta算法.给出了一个数值计算实例,从结果可以说明这种方法的可行,也体现了辛算法对系统的能量具有良好的守恒性.

The resoluUon of differential games often concerns the difficult problem of Two Point Border Value （TPBV）, then ascribe linear quadratic differential game to Hamilton system, To Hamilton system, the algorithm of symplectic geometry has the merits of being able to copy the dynamic structure of Hamilton system and to keep the measure of phase plane. From the point of view of Hamilton system, the symplectic characters of linear quadratic differential game were probed; And as a try, Symplectic-Runge-Kutta algorithm was inducted to the resolution of infinite horizon linear quadratic differential game.An example of numerical calculation was presented,and the result can illuminate the feasiblity of this method. At the same time, it embodies the fine conservation characteristics of symplectic algorithm to system energy.