Contrôle optimal d'équations différentielles avec - ou sans - mémoire

Xavier Dupuis 1, 2
2 Commands - Control, Optimization, Models, Methods and Applications for Nonlinear Dynamical Systems
CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique, Inria Saclay - Ile de France, UMA - Unité de Mathématiques Appliquées
Abstract : The thesis addresses optimal control problems where the dynamics is given by differential equations with memory. For these optimization problems, optimality conditions are provided; second order conditions constitute an important part of the results of the thesis. In the case - without memory - of ordinary differential equations, standard optimality conditions are strengthened by involving only the Lagrange multipliers for which Pontryagin's principle is satisfied. This restriction to a subset of multipliers represents a challenge in the establishment of necessary conditions and enables sufficient conditions to assure local optimality in a stronger sense. Standard conditions are on the other hand extended to the case - with memory - of integral equations. Pure state constraints of the previous problem have been kept and require a specific study due to the integral dynamics. Another form of memory in the state equation of an optimal control problem comes from a modeling work with therapeutic optimization as a medical application in view. Cancer cells populations dynamics under the action of a treatment is reduced to delay differential equations; the long time asymptotics of the age-structured model is also studied.
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Submitted on : Thursday, December 5, 2013 - 10:40:08 AM
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  • HAL Id : tel-00914246, version 1


Xavier Dupuis. Contrôle optimal d'équations différentielles avec - ou sans - mémoire. Optimisation et contrôle [math.OC]. Ecole Polytechnique X, 2013. Français. ⟨tel-00914246⟩



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