SINGULAR PERTURBATION OF A FINITE-HORIZON PROBLEM WITH STATE-SPACE CONSTRAINTS

We study the singular perturbation of optimal control problems for non linear systems with constraints on the fast state variables and a cost functional either of Bolza type or involving the exit time of the sys tem from a given domain. Under a controllability assumption on the fas t variables, we show that these variables become controls in the limit problem. Our method consists of passing to the limit in the associate d Hamilton-Jacobi-Bellman (HJB) equations by means of some tools in th e theory of viscosity solutions.