On some optimal control problems governed by a state equation with memory
Université Paris Dauphine, CEREMADE, Pl. de Lattre de Tassigny, 75775 Paris Cedex 16, France; email@example.com; firstname.lastname@example.org
Revised: 20 March 2007
The aim of this paper is to study problems of the form: with where V is a set of admissible controls and yu is the solution of the Cauchy problem: , and each is a nonnegative measure with support in [0,t]. After studying the Cauchy problem, we establish existence of minimizers, optimality conditions (in particular in the form of a nonlocal version of the Pontryagin principle) and prove some regularity results. We also consider the more general case where the control also enters the dynamics in a nonlocal way.
Mathematics Subject Classification: 34K35 / 49K25
Key words: Optimal control / memory
© EDP Sciences, SMAI, 2008