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Approximation of controlproblems involving ordinary and impulsive controls

Published online by Cambridge University Press:  15 August 2002

Fabio Camilli  and
Maurizio Falcone
Fabio Camilli
Affiliation:
Dipartimento di Matematica, Università di Torino, Via Carlo Alberto 10, 10123 Torino, Italy; Camilli@dm.unito.it.
Maurizio Falcone
Affiliation:
Dipartimento di Matematica, Università di Roma “La Sapienza", P.le Aldo Moro 2, 00185 Roma, Italy; Falcone@axcasp.caspur.it.
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Abstract

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∞ 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.

Keywords

Impulsive controlapproximation schemedynamic programmingviscosity solution
Type
Research Article
Information
ESAIM: Control, Optimisation and Calculus of Variations , Volume 4 , 1999 , pp. 159 - 176
Copyright
© EDP Sciences, SMAI, 1999

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