Free-Endpoint Optimal Control of Inhomogeneous Bilinear Ensemble Systems

TL;DR

This paper introduces an iterative method for solving optimal control problems involving inhomogeneous bilinear ensemble systems with free-endpoint conditions, applicable to deterministic and stochastic systems, with demonstrated success in neuroscience and quantum control.

Contribution

It develops a novel iterative approach that transforms bilinear ensemble control problems into linear ones at each step, ensuring convergence and optimality, and extends applicability to stochastic systems.

Findings

Method successfully controls neuroscience systems.

Applicable to quantum control scenarios.

Proven convergence and robustness.

Abstract

Optimal control of bilinear systems has been a well-studied subject in the areas of mathematical and computational optimal control. However, effective methods for solving emerging optimal control problems involving an ensemble of deterministic or stochastic bilinear systems are underdeveloped. These burgeoning problems arise in diverse applications from quantum control and molecular imaging to neuroscience. In this work, we develop an iterative method to find optimal controls for an inhomogeneous bilinear ensemble system with free-endpoint conditions. The central idea is to represent the bilinear ensemble system at each iteration as a time-varying linear ensemble system, and then solve it in an iterative manner. We analyze convergence of the iterative procedure and discuss optimality of the convergent solutions. The method is directly applicable to solve the same class of optimal control problems involving a stochastic bilinear ensemble system driven by independent additive noise processes. We demonstrate the robustness and applicability of the developed iterative method through practical control designs in neuroscience and quantum control.