6533b82efe1ef96bd12927e0

RESEARCH PRODUCT

Optimal control of an ensemble of Bloch equations with applications in MRI

Alain JacquemardBernard BonnardJérémy Rouot

subject

[ MATH.MATH-OC ] Mathematics [math]/Optimization and Control [math.OC]0209 industrial biotechnologySpins010102 general mathematicsNuclear resonance[MATH.MATH-OC] Mathematics [math]/Optimization and Control [math.OC]02 engineering and technologyOptimal controlLinear-quadratic-Gaussian control01 natural sciences020901 industrial engineering & automationMaximum principleControl theoryBloch equationsApplied mathematics[MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC]Boundary value problem0101 mathematicsComputingMilieux_MISCELLANEOUSMathematics

description

International audience; The optimal control of an ensemble of Bloch equations describing the evolution of an ensemble of spins is the mathematical model used in Nuclear Resonance Imaging and the associated costs lead to consider Mayer optimal control problems. The Maximum Principle allows to parameterize the optimal control and the dynamics is analyzed in the framework of geometric optimal control. This lead to numerical implementations or suboptimal controls using averaging principle.

yearjournalcountryeditionlanguage
2016-12-122016 IEEE 55th Conference on Decision and Control (CDC)
https://doi.org/10.1109/cdc.2016.7798495