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H. Yilmaz:
"Contributions à la théorie du Contrôle Optimal (Contributions to the theory of Optimal Control)";
Supervisor, Reviewer: J. Blot, S. Scotti, A. Daniilidis; Université de Paris - SCIENCES MATHEMATIQUES DE PARIS CENTRE 386, 2021; oral examination: 2021-12-02.

This thesis is made up of contributions to the theory of Optimal Control within the framework of
the Pontryagin Maximum Principle for a system governed by an ordinary differential equation, with
piecewise continuous control functions and piecewise continuously differentiable state functions.
A first contribution is an improvement of this principle of Pontryagin which consists in lightening
the assumptions of the existing results in this framework.
A second contribution is to establish Envelope Theorems in this framework. This type of theorem
is considered especially important in theoretical economics.
The realization of these contributions uses recent Multiplier Rules (one of which is original), uses
the establishment of a Functional analysis framework which makes it possible to define efficient
operators and functionals, uses the rigorous justification of the theorems on ordinary differential
equations with piecewise continuously differentiable solutions, and uses new results on nonlinear
functionals in integral form.

Optimal Control, Pontryagin maximum principle, Envelope Theorem, Calculus of Variations, Static optimization, Ordinary differential equations.