a1 Université Paris Dauphine, CEREMADE, Pl. de Lattre de Tassigny, 75775 Paris Cedex 16, France. firstname.lastname@example.org ; email@example.com
This article is devoted to the optimal control of state equations with memory of the form:
with initial conditions .
Denoting by the solution of the previous Cauchy problem and:
where V is a class of admissible controls, we prove that v is the only viscosity solution of an Hamilton-Jacobi-Bellman equation of the form:
in the sense of the theory of viscosity solutions in infinite-dimensions of Crandall and Lions.
(Received March 21 2008)
(Revised March 26 2009)
(Online publication July 31 2009)
Mathematics Subject Classification: