We study convergence of value-functions associated to control systems with a singular perturbation. In the nonlinear case, we prove new convergence results: the limit of optimal costs of the perturbed system is an optimal cost for the reduced system. We furthermore provide an estimation of the rate of convergence when the solutions of the reduced are regular enough
"Singular perturbations in non-linear optimal control systems." Differential Integral Equations 8 (4) 931 - 944, 1995.