6533b862fe1ef96bd12c73e7

RESEARCH PRODUCT

Algebraic-geometric techniques for the feedback classification and robustness of the optimal control of a pair of Bloch equations with application to Magnetic Resonance Imaging

Bernard BonnardOlivier CotsJean-charles FaugèreAlain JacquemardJérémy RouotMohab Safey El DinThibaut Verron

subject

[ MATH.MATH-OC ] Mathematics [math]/Optimization and Control [math.OC]optimal controlMSC. 49K15 14Q20 81Q93[MATH.MATH-OC] Mathematics [math]/Optimization and Control [math.OC]singular trajectories[MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC]Bloch equationsMagnetic Resonance Imagingsymbolic computation

description

The aim of this article is to classify the singular trajectories associated with the optimal control problems of a pair of controlled Bloch equations. The motivation is to analyze the robustness of the optimal solutions to the contrast and the time-minimal saturation problem, in magnetic resonance imaging, with respect to the parameters and B1-inhomogeneity. For this purpose, we use various computer algebra algorithms and methods to study solutions of polynomial systems of equations and inequalities which are used for classification issues: Gröbner basis, cylindrical algebraic decomposition of semi-algebraic sets, Thom's isotopy lemma.

yearjournalcountryeditionlanguage
2017-01-01
https://hal.inria.fr/hal-01556806/document