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Geometric Optimal Control of the Contrast Imaging Problem in Nuclear Magnetic Resonance

By Bernard Bonnard, Olivier Cots, Steffen Glaser, Marc Lapert, Dominique Sugny and Yun Zhang

Abstract

International audienceThe objective of this article is to introduce the tools to analyze the contrast imaging problem in Nuclear Magnetic Resonance. Optimal trajectories can be selected among extremal solutions of the Pontryagin Maximum Principle applied to this Mayer type optimal problem. Such trajectories are associated to the question of extremizing the transfer time. Hence the optimal problem is reduced to the analysis of the Hamiltonian dynamics related to singular extremals and their optimality status. This is illustrated by using the examples of cerebrospinal fluid/water and grey/white matter of cerebrum

Topics: SYSTEMS, EXTREMALS, DESIGN, RELAXATION, DYNAMICAL SEMIGROUPS, BAND EXCITATION PULSES, NMR, [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC]
Publisher: 'Institute of Electrical and Electronics Engineers (IEEE)'
Year: 2012
DOI identifier: 10.1109/TAC.2012.2195859
OAI identifier: oai:HAL:hal-00750032v1
Provided by: HAL-uB
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