On the proof of Michel of the maximum Pontryagin Principle

Joël Blot (1) , Hasan Yilmaz

1 SAMM - Statistique, Analyse et Modélisation Multidisciplinaire (SAmos-Marin Mersenne)

We provide an improvment of the maximum principle of Pon-tryagin of the optimal control problems, for a system governed by an ordinary differential equation, in presence of final constraints, in the setting of the piece-wise differentiable state functions (valued in a Banach space) and of piecewise continuous control functions (valued in a metric space). As Michel we use the needlelike variations, but we introduce tools of functional analysis and a recent multiplier rule of the static optimization to make our proofs. Mathematical Subject Classification 2010: 49K15, 47H10

Mots clés: Pontryagin maximum principle; piecewise continuous functions; fixed point theorem

Domaines: Optimisation et contrôle [math.OC]

Joël Blot, Hasan Yilmaz. On the proof of Michel of the maximum Pontryagin Principle. 2019. ⟨hal-02086774⟩