Fixed-Endpoint Optimal Control of Bilinear Ensemble Systems

TL;DR

This paper introduces an iterative method for solving optimal control problems involving ensembles of bilinear systems, transforming them into linear ensemble problems and deriving control laws via singular value expansion, with applications in magnetic resonance.

Contribution

The paper develops a novel iterative approach for optimal control of bilinear ensemble systems, including convergence analysis and practical magnetic resonance applications.

Findings

Effective iterative solution for bilinear ensemble control problems

Convergence and optimality conditions established

Demonstrated robustness in magnetic resonance control design

Abstract

Optimal control of bilinear systems has been a well-studied subject in the area of mathematical control. However, techniques for solving emerging optimal control problems involving an ensemble of structurally identical bilinear systems are underdeveloped. In this work, we develop an iterative method to effectively and systematically solve these challenging optimal ensemble control problems, in which the bilinear ensemble system is represented as a time-varying linear ensemble system at each iteration and the optimal ensemble control law is then obtained by the singular value expansion of the input-to-state operator that describes the dynamics of the linear ensemble system. We examine the convergence of the developed iterative procedure and pose optimality conditions for the convergent solution. We also provide examples of practical control designs in magnetic resonance to demonstrate the applicability and robustness of the developed iterative method.