Abstract
We present some applications of geometric optimal control theoryto control problems in Nuclear Magnetic Resonance (NMR) andMagnetic Resonance Imaging (MRI). Using the Pontryagin MaximumPrinciple (PMP), the optimal trajectories are found as solutionsof a pseudo-Hamiltonian system. This computation can be completedby second-order optimality conditions based on the concept ofconjugate points. After a brief physical introduction to NMR, thisapproach is applied to analyze two relevant optimal control issuesin NMR and MRI: the control of a spin 1/2 particle in presence ofradiation damping effect and the maximization of the contrast inMRI. The theoretical analysis is completed by numericalcomputations. This work has been made possible by the central andessential role of B. Bonnard, who has been at the heart of thisproject since 2009.
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