Comparison of Numerical Methods in the Contrast Imaging Problem in NMR

Bernard Bonnard 1 Mathieu Claeys 2 Olivier Cots 3 Pierre Martinon 4, 5
2 LAAS-MAC - Équipe Méthodes et Algorithmes en Commande
LAAS - Laboratoire d'analyse et d'architecture des systèmes [Toulouse]
3 McTAO - Mathematics for Control, Transport and Applications
CRISAM - Inria Sophia Antipolis - Méditerranée
5 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 : In this article, the contrast imaging problem in nuclear magnetic resonance is modeled as a Mayer problem in optimal control. A first synthesis of locally optimal solutions is given in the single-input case using geometric methods based on Pontryagin's maximum principle. We then compare these results using direct methods and a moment-based approach, and make a first step towards global optimality. Finally, some preliminary results are given in the bi-input case.
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Submitted on : Wednesday, March 13, 2013 - 4:24:58 PM
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Bernard Bonnard, Mathieu Claeys, Olivier Cots, Pierre Martinon. Comparison of Numerical Methods in the Contrast Imaging Problem in NMR. 52nd IEEE Conference on Decision and Control, Dec 2013, Firenze, Italy. ⟨hal-00800436⟩



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