Distance estimates for state constrained trajectories of infinite dimensional differential inclusions

Hélène Frankowska (1, 2) , Elsa M Marchini (3) , Marco Mazzola (4)

1 C&O - Equipe combinatoire et optimisation
2 IMJ-PRG (UMR_7586) - Institut de Mathématiques de Jussieu - Paris Rive Gauche
3 Dipartimento di Matematica "F. Brioschi"
4 IMJ - Institut de Mathématiques de Jussieu

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.

Mots clés: Semilinear differential inclusion; state constraint; relaxation theorem; neighboring feasible trajectory theorem

Domaines: Mathématiques [math]; Optimisation et contrôle [math.OC]

Hélène Frankowska, Elsa M Marchini, Marco Mazzola. Distance estimates for state constrained trajectories of infinite dimensional differential inclusions. ESAIM: Control, Optimisation and Calculus of Variations, 2018, 24 (3), pp.1207-1229. ⟨10.1051/cocv/2017032⟩. ⟨hal-02126117⟩