Approximation of control problems involving ordinary and impulsive controls

In this paper we study an approximation scheme for a class of control problems involving an ordinary control v, an impulsive control u and its derivative u_ . Adopting a space-time reparametrization of the problem which adds one variable to the state space we overcome some diculties connected to the presence of u_ . We construct an approximation scheme for that augmented system, prove that it converges to the value function of the augmented problem and establish an error estimates in L1 for this approximation. Moreover, a characterization of the limit of the discrete optimal controls is given showing that it converges (in a suitable sense) to an optimal control for the continuous problem