O.-S. Serea & F. Watbled
"Convergence of Discontinuous Value Functions of Singularly Perturbed
Control Systems with terminal or infimum cost."
We prove that the discontinuous value function of an optimal control problem
with terminal or infimum cost for a control system with a singular
perturbation converges to the discontinuous value function of an optimal
control problem associated with the control system obtained by averaging. The
main novelty here is the discontinuity of the cost.