M. Quincampoix & F. Watbled
"Averaging method for discontinuous Mayer's problem of singularly
perturbed control systems."
In the present paper, we prove that the optimal cost of a
Mayer's problem for
a control system with singular perturbation does converge
to the optimal cost of
a Mayer's 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.