Search results for "Contrast imaging in NMR"

showing 2 items of 2 documents

Geometric optimal control : homotopic methods and applications

2012

This work is about geometric optimal control applied to celestial and quantum mechanics. We first dealt with the minimum fuel consumption problem of transfering a satellite around the Earth. This brought to the creation of the code HamPath which permits first of all to solve optimal control problem for which the command law is smooth. It is based on the Pontryagin Maximum Principle (PMP) and on the notion of conjugate point. This program combines shooting method, differential homotopic methods and tools to compute second order optimality conditions. Then we are interested in quantum control. We study first a system which consists in two different particles of spin 1/2 having two different r…

[SPI.OTHER]Engineering Sciences [physics]/OtherMéthodes de tirHomotopie différentielle[ SPI.OTHER ] Engineering Sciences [physics]/OtherOrbital transferContrôle optimal géométrique[SPI.OTHER] Engineering Sciences [physics]/Other[ MATH.MATH-GM ] Mathematics [math]/General Mathematics [math.GM]Shooting methodsDifferential homotopyAutomatic differentiationContraste en RMNQuantum control[MATH.MATH-GM] Mathematics [math]/General Mathematics [math.GM]Geometric optimal controlConditions du deuxième ordreTransfert orbitalLieux conjugués et de coupureDifférenciation automatiqueSecond order conditions[MATH.MATH-GM]Mathematics [math]/General Mathematics [math.GM]Cut and conjugate lociContrast imaging in NMRContrôle quantique
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A combination of algebraic, geometric and numerical methods in the contrast problem by saturation in magnetic resonance imaging

2014

In this article, the contrast imaging problem by saturation 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 recent advanced techniques of geometric optimal control. This leads to a numerical investigation based on shooting and continuation methods implemented in the HamPath software. The results are compared with a direct approach to the optimization problem and implemented within the Bocop toolbox. In complement lmi techniques are used to estimate a global optimum. It is completed with the analysis of the saturation problem of an ensemble of spin particle…

[ MATH.MATH-OC ] Mathematics [math]/Optimization and Control [math.OC]Moment optimization[MATH.MATH-OC] Mathematics [math]/Optimization and Control [math.OC]Direct methodContrast imaging in NMR[MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC]Geometric optimal controlShooting and continuation techniques
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