Hamilton-Jacobi-Bellman equations for the optimal control of a state equation with memory
Université Paris Dauphine, CEREMADE, Pl. de Lattre de Tassigny, 75775 Paris Cedex 16, France. firstname.lastname@example.org ; email@example.com
Revised: 26 March 2009
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.
Mathematics Subject Classification: 49L20 / 49L25
Key words: Dynamic programming / state equations with memory / viscosity solutions / Hamilton-Jacobi-Bellman equations in infinite dimensions
© EDP Sciences, SMAI, 2009