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Mesures d'occupation et relaxations semi-définies pour la commande optimale

Mathieu Claeys 1
1 LAAS-MAC - Équipe Méthodes et Algorithmes en Commande
LAAS - Laboratoire d'analyse et d'architecture des systèmes
Abstract : This thesis details a global method for optimal control of open-loop systems. This is done by relaxing the control problem as a generalized moment problem, which can be solved numerically by a hierarchy of semi-definite relaxations. The approach is first applied to the impulsive control of linear time varying systems, by modeling the controls by a measure. The resulting semi-definite conditions circumvent time discretiziation and related difficulties. By the use of occupation measures, the method is then extended to a class of impulsive non-linear problems. This results in a monotone sequence of lower bounds to the original control problem. Finally, those results are transposed to switched system, by modeling each mode by a corresponding occupation measure. This allows for large computational gains with respect to the classical approach, where the control space is measured.
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Submitted on : Friday, October 25, 2013 - 9:44:47 AM
Last modification on : Thursday, June 10, 2021 - 3:07:04 AM
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  • HAL Id : tel-00876609, version 1

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Mathieu Claeys. Mesures d'occupation et relaxations semi-définies pour la commande optimale. Optimisation et contrôle [math.OC]. INSA de Toulouse, 2013. Français. ⟨tel-00876609⟩

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