0000000000585148

AUTHOR

Olivier Cots

showing 3 related works from this author

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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Differential pathfollowing for regular optimal control problems

2012

International audience

[ MATH.MATH-OC ] Mathematics [math]/Optimization and Control [math.OC][MATH.MATH-OC] Mathematics [math]/Optimization and Control [math.OC][MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC]ComputingMilieux_MISCELLANEOUS
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Working Notes on the Time Minimal Saturation of a Pair of Spins and Application in Magnetic Resonance Imaging

2018

In this article, we analyse the time minimal control for the saturation of a pair of spins of the same species but with inhomogeneities of the applied RF-magnetic field, in relation with the contrast problem in Magnetic Resonance Imaging. We make a complete analysis based on geometric control to classify the optimal syntheses in the single spin case to pave the road to analyze the case of two spins. The Bocop software is used to determine local minimizers for physical test cases and Linear Matrix Inequalities approach is applied to estimate the global optimal value and validate the previous computations. This is complemented by numerical computations combining shooting and continuation meth…

[ MATH.MATH-OC ] Mathematics [math]/Optimization and Control [math.OC][MATH.MATH-OC] Mathematics [math]/Optimization and Control [math.OC][MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC]
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