A Generalization of Michel’s Result on the Pontryagin Maximum Principle

Abstract

We provide an improvement of the maximum principle of Pontryagin of the optimal control problems, for a system governed by an ordinary differential equation, in the presence of final constraints, in the setting of the piecewise continuously 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.