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. Let T and T(h) be the minimal time functions to reach the origin of two control systems y' = f(y, a) and y' = f(h)(y, a), both locally controllable in the origin, and let K be any compact set of points controllable to the origin. If parallel-to f(h) - f parallel-to infinity less-than-or-equal-to Ch, then \T(x) - T(h)(x)\ less-than-or-equal-to C(k)h-alpha, for all x is-an-element-of K, where alpha is the exponent of Holder continuity of T(x).