Approximation of control problems involving ordinary and impulsive controls

摘要

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