The pioneering works concerning control problems governed by ordinary differential equations and evolution inclusions with Young measures are due to C.Castaing, P.Raynaud de Fitte and A.Jofre [see 17, 16 in the references]. In the same spirit, we consider in this paper some Bolza-type problems governed by two classes of functional evolutions inclusions, where the controls are Young measures. In particular, we present some variational properties of the value function of these dynamics and we show that the lower value function associated to a continuous cost functional is a viscosity sub-solutions of the corresponding Hamilton-Jacobi-Bellman equation. This sheds a new light in the study of the viscosity solutions for the dynamics governed by ordinary differential equations. In the present paper we also extend a number of results in the literature of evolution inclusions and ordinary differential equations.

Control problems governed by functional evolution inclusions with Young measures

SALVADORI, Anna
2004

Abstract

The pioneering works concerning control problems governed by ordinary differential equations and evolution inclusions with Young measures are due to C.Castaing, P.Raynaud de Fitte and A.Jofre [see 17, 16 in the references]. In the same spirit, we consider in this paper some Bolza-type problems governed by two classes of functional evolutions inclusions, where the controls are Young measures. In particular, we present some variational properties of the value function of these dynamics and we show that the lower value function associated to a continuous cost functional is a viscosity sub-solutions of the corresponding Hamilton-Jacobi-Bellman equation. This sheds a new light in the study of the viscosity solutions for the dynamics governed by ordinary differential equations. In the present paper we also extend a number of results in the literature of evolution inclusions and ordinary differential equations.
2004
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11391/10096
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