Discrete time pontryagin principles in banach spaces

Mohammed Bachir (1) , Joël Blot (2)

1 Equations d'evolution
2 SAMM - Statistique, Analyse et Modélisation Multidisciplinaire (SAmos-Marin Mersenne)

The aim of this paper is to establish Pontryagin's principles in a dicrete-time infinite-horizon setting when the state variables and the control variables belong to infinite dimensional Banach spaces. In comparison with previous results on this question, we delete conditions of finiteness of codi-mension of subspaces. To realize this aim, the main idea is the introduction of new recursive assumptions and useful consequences of the Baire category theorem and of the Banach isomorphism theorem.

Mots clés: Pontryagin principle; discrete time; infinite horizon; difference equa-; tion; Banach spaces; MSC 2000: 49J21; 65K05; 39A99

Domaines: Optimisation et contrôle [math.OC]; Analyse fonctionnelle [math.FA]

Mohammed Bachir, Joël Blot. Discrete time pontryagin principles in banach spaces. 2017. ⟨hal-01524112⟩