On the application of geometric optimal control theory to nuclear magnetic resonance

Elie Assémat, Marc Lapert, Dominique Sugny, Steffen J. Glaser

Research output: Contribution to journalArticlepeer-review

7 Scopus citations

Abstract

We present some applications of geometric optimal control theory to control problems in Nuclear Magnetic Resonance (NMR) and Magnetic Resonance Imaging (MRI). Using the Pontryagin Maximum Principle (PMP), the optimal trajectories are found as solutions of a pseudo-Hamiltonian system. This computation can be completed by second-order optimality conditions based on the concept of conjugate points. After a brief physical introduction to NMR, this approach is applied to analyze two relevant optimal control issues in NMR and MRI: the control of a spin 1/2 particle in presence of radiation damping effect and the maximization of the contrast in MRI. The theoretical analysis is completed by numerical computations. This work has been made possible by the central and essential role of B. Bonnard, who has been at the heart of this project since 2009.

Original languageEnglish
Pages (from-to)375-396
Number of pages22
JournalMathematical Control and Related Fields
Volume3
Issue number4
DOIs
StatePublished - 2013

Keywords

  • Contrast problem
  • Geometrical optimal control
  • Nuclear magnetic resonance
  • Pontryagin maximum principle

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