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 leads to numerical implementations or suboptimal controls using averaging principle.
['Bernard Bonnard', 'Alain Jacquemard', 'Jérémy Rouot']
Optimal control of an ensemble of Bloch equations with applications in MRI