Contrôle optimal et calcul des variations en présence de retard sur l'état.

Abstract : In this thesis, we have attempted to contribute to the optimization of dynamical problems with delay in state space. We are specifically interested in the viewpoint of Pontryagin who outlined in his book published in 1962 the necessary conditions required for solving such problems. In his work published in 1972, Warga catalogued the possible solutions. Li and al. analyzed the case of periodic control. We will treat an optimal control problem governed by a Delay Functional Differential Equation. Our method is close to the one of P. Michel on dynamical system governed by Ordinary Differential Equations. The main problem ariving out in this approach is the use of the resolvent of the Delay Functional Differential Equation. We also consider Euler-Lagrange condition in the framework of variational problems with delay.
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Mamadou Ibrahima Koné. Contrôle optimal et calcul des variations en présence de retard sur l'état.. Optimisation et contrôle [math.OC]. Université Paris 1 - Panthéon Sorbonne, 2016. Français. ⟨tel-01499422⟩

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