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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https://hal.inria.fr/hal-00867753
Contributor : Pierre Martinon <>
Submitted on : Monday, September 30, 2013 - 2:51:21 PM
Last modification on : Wednesday, July 3, 2019 - 10:48:03 AM
Long-term archiving on : Friday, April 7, 2017 - 4:35:43 AM

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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. 2013. ⟨hal-00867753v1⟩

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