ON THE APPLICATION OF GEOMETRIC OPTIMAL CONTROL THEORY TO NUCLEAR MAGNETIC RESONANCE

被引：7

作者：

Assemat, Elie ^{[1
]}

Lapert, Marc ^{[1
]}

Sugny, Dominique ^{[1
]}

Glaser, Steffen J. ^{[2
]}

机构：

[1] Univ Bourgogne, CNRS, UMR 5209, Lab Interdisciplinaire Carnot Bourgogne ICB, F-21078 Dijon, France

[2] Tech Univ Munich, Dept Chem, D-85747 Garching, Germany

来源：

MATHEMATICAL CONTROL AND RELATED FIELDS | 2013年 / 3卷 / 04期

关键词：

Geometrical optimal control; Nuclear Magnetic Resonance; Pontryagin Maximum Principle; contrast problem; BROAD-BAND EXCITATION; IMAGING PROBLEM; SPIN DYNAMICS; PULSES; INVERSION; DESIGN; SPECTROSCOPY; TRAJECTORIES; SYSTEMS; LIMITS;

D O I：

10.3934/mcrf.2013.3.375

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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.

引用

页码：375 / 396

页数：22

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