半线性发展方程支配的微分博弈鞍点的通有唯一性

Generic Uniqueness of Saddle Point for Differential Games Governed by Semi-Linear Evolution Equation

应用集值分析方法,研究半线性发展方程支配的微分博弈鞍点的稳定性,证明了半线性发展方程支配的微分博弈关于控制系统右端函数发生扰动时,对应的鞍点具有通有唯一性,也就是在Baire纲分类意义下,大多数半线性发展方程支配的微分博弈的鞍点具有唯一解。

In this paper, the generic uniqueness of saddle point for differential games governed by semi-linear evolution equation is studied. By employing the method of set-valued analysis, we prove that, the generic uniqueness of differential games governed by semi-linear evolution equation with respect to perturb function of the right-hand control system, that is, most of differential games governed by semi-linear evolution equation exist unique solution, in the sense of Baire’s category.