Averaging method for discontinuous Mayerʹs problem of singularly perturbed control systems Original Research Article

In the present paper, we prove that the optimal cost of a Mayerʹs problem for a control system with singular perturbation does converge to the optimal cost of a Mayerʹs problem associated with control system obtained by averaging. The main novelty of our result lies on the fact that we did not require any continuity assumption on the final cost.