Geometric and numerical methods in the contrast imaging problem in nuclear magnetic resonance

Bernard Bonnard 1, * Mathieu Claeys 2 Olivier Cots 3 Pierre Martinon 4, 5
* Corresponding author
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. The optimal solution can be found as an extremal, solution of the Maximum Principle and analyzed with the techniques of geometric control. This leads to a numerical investigation based on so-called indirect methods using the HamPath software. The results are then compared with a direct method implemented within the Bocop toolbox. Finally lmi techniques are used to estimate a global optimum.
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Bernard Bonnard, Mathieu Claeys, Olivier Cots, Pierre Martinon. Geometric and numerical methods in the contrast imaging problem in nuclear magnetic resonance. Acta Applicandae Mathematicae, Springer Verlag, 2015, 135 (1), pp.5-45. ⟨10.1007/s10440-014-9947-3⟩. ⟨hal-00867753v2⟩

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