Distance estimates for state constrained trajectories of infinite dimensional differential inclusions^★

¹ CNRS, Institut de Mathématiques de Jussieu - Paris Rive Gauche, UMR 7586, Sorbonne Universités, UPMC Univ Paris 06, Univ Paris Diderot, Sorbonne Paris Cité, Case 247, 4 Place Jussieu, 75252 Paris, France
² Dipartimento di Matematica “F.Brioschi”, Politecnico di Milano, Piazza Leonardo da Vinci 32, 20133 Milano, Italy.
³ Sorbonne Universités, UPMC Univ Paris 06, Institut de Mathématiques de Jussieu - Paris Rive Gauche, UMR 7586, CNRS, Univ Paris Diderot, Sorbonne Paris Cité, Case 247, 4 Place Jussieu, 75252 Paris, France.

^* Corresponding author: elsa.marchini@polimi.it

Received: 26 February 2017
Accepted: 19 April 2017

Abstract

This paper concerns estimates on the distance between a trajectory of a differential inclusion and the set of feasible trajectories of the same inclusion, feasible meaning confined to a given set of constraints. We apply these estimates to investigate Lipschitz continuity of the value functions arising in optimal control, and to variational inclusions, useful for proving non degenerate necessary optimality conditions. The main feature of our analysis is the infinite dimensional framework, which can be applied to models involving PDEs.