Fixed-endpoint minimum-energy control of bilinear ensemble systems

Optimal control of bilinear systems has been a well-studied subject in the area of mathematical control. However, effective methods for solving the emerging optimal control problems involving an ensemble of bilinear systems are underdeveloped. In this work, we present an iterative method to effectively solve these challenging optimal control problems, in which at each iteration the bilinear ensemble system is represented as a time-varying linear ensemble system and then the optimal ensemble control is obtained by using an SVD-based computational algorithm designed for solving optimal control problems for linear ensemble systems. We analyze the convergence of the developed iterative method and provide examples of practical ensemble control designs in magnetic resonance to demonstrate its applicability.