On the value function of singularly perturbed optimal control systems

The convergence of the value function of a singularly perturbed optimal control problem to the value function of an appropriately chosen variational limit problem examined. The limit problem is determined by the limit distributions of the control and the state on the fast time scale. The desired convergence follows from regularity properties of the limit problem. A byproduct of the proof is a scheme of constructing near optimal solutions to the perturbed problem from solutions of the limit problem.