Optimal Control of Distributed Ensembles With Application to Bloch Equations

Motivated by the problem of designing robust composite pulses for Bloch equations in the presence of natural perturbations, we study an abstract optimal ensemble control problem in a probabilistic setting with a general nonlinear performance criterion. The model under study addresses mean-field dynamics described by a linear continuity equation in the space of probability measures. For the resulting optimization problem, we derive an exact representation of the increment of the cost functional in terms of the flow of the driving vector field. Using this representation, a descent method is designed that is free of any internal line search. The method is applied to solve new optimal control problems for distributed ensembles of Bloch equations.