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Problèmes de contrôle optimal du type bilinéaire gouvernés par des équations aux dérivées partielles d’évolution

Abstract : This thesis is devoted to the analysis of nonlinear optimal control problems governed by an evolution state equation involving a term which is bilinear in state and control. The difficulties due to nonlinearity remain, but bilinearity adds a lot of structure to the control problem under consideration. In Section 2, by using Willet and Wong inequalities we establish a priori estimates for the solutions of the state equation. These estimates allow us to prove that the state equation is well posed in the sense of Hadamard. In the case of a feedback constraint on the control, the state equation becomes a differential inclusion. Under mild assumptions, such a differential inclusion is solvable. In Section 3, we prove the existence of solutions to the optimal control problem. Section 4 is devoted to the sensitivity analysis of the optimal control problem. We obtain a formula for the directional derivative of the optimal value function. This general formula is worked out in detail for particular examples
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Jean-Marc Clérin. Problèmes de contrôle optimal du type bilinéaire gouvernés par des équations aux dérivées partielles d’évolution. Mathématiques générales [math.GM]. Université d'Avignon, 2009. Français. ⟨NNT : 2009AVIG0405⟩. ⟨tel-00453643⟩

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