Sensitivity analysis of an optimal control problem under Lipschitzian perturbations

Abstract

In this paper, we study the quantitative stability of an optimal control problem with respect to parametric perturbations.We essentially obtain two equivalent conclusions for the stability of this problem by using two independent methods.The first one makes recourse to standard computations based on the famous Gronwall Lemma while our second method employees rather stability of fixed points trough the celebrated Lim's Lemma for which we construct a suitable contracting set-valued mapping over a larger functional space than the one of continuous functions adopted in the close previous works.The second method allows us to introduce a further concept of approximate solutions regarded as approximate values of the optimal control for which we prove similar stability properties as in the case of exact solutions.