Approximation and regular perturbation of optimal control problems via Hamilton-Jacobi theory

We present two convergence theorems for Hamilton-Jacobi equations and we apply them to the convergence of approximations and perturbations of optimal control problems and of two-players zero-sum differential games. One of our results is, for instance, the following. LetT andT_h be the minimal time functions to reach the origin of two control systemsy = f(y, a) andy = f_h(y, a), both locally controllable in the origin, and letK be any compact set of points controllable to the origin. If f_h –f Ch, then |T(x) – T_h(x)| C_Kh, for all x K, where is the exponent of Hölder continuity ofT(x).