Optimal Control of an Ensemble of Bloch Equations with Applications in MRI

Bernard Bonnard 1, 2 Alain Jacquemard 1, 3 Jérémy Rouot 2
2 McTAO - Mathematics for Control, Transport and Applications
CRISAM - Inria Sophia Antipolis - Méditerranée
3 PolSys - Polynomial Systems
LIP6 - Laboratoire d'Informatique de Paris 6, Inria de Paris
Abstract : 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.
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Bernard Bonnard, Alain Jacquemard, Jérémy Rouot. Optimal Control of an Ensemble of Bloch Equations with Applications in MRI. 55th IEEE Conference on Decision and Control - CDC, Dec 2016, Las Vegas, United States. pp.1608-1613, ⟨10.1109/CDC.2016.7798495⟩. ⟨hal-01287290v4⟩

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