Approximation of control problems involving ordinary and impulsive controls
Camilli, Fabio; Falcone, Maurizio; Camilli Fabio; Dipartimento di Matematica, Università di Torino, Via Carlo Alberto 10, 10123 Torino, Italy; Camilli@dm.unito.it.; Falcone Maurizio; Dipartimento di Matematica, Università di Roma “La Sapienza", P.le Aldo Moro 2, 00185 Roma, Italy; Falcone@axcasp.caspur.it.
Журнал:
ESAIM: Control, Optimisation and Calculus of Variations
Дата:
1999
Аннотация:
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 $\dot u$. Adopting a space-time reparametrization of the problem which adds one variable to the state space we overcome some difficulties connected to the presence of $\dot u$. 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 L <sup>∞</sup> 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.
436.0Кб