Moment-Based Ensemble Control

TL;DR

This paper introduces a novel moment-based framework for controlling large populations of dynamical systems, leveraging moments in probability theory to address underactuation and limited feedback challenges.

Contribution

It extends the method of moments to control theory, establishing an equivalence between ensemble and moment systems for controllability and feedback control design.

Findings

Established controllability equivalence between ensemble and moment systems

Developed moment-feedback control laws for ensemble systems

Validated control approach mathematically and numerically

Abstract

Controlling a large population, in the limit, a continuum, of structurally identical dynamical systems with parametric variations is a pervasive task in diverse applications in science and engineering. However, the severely underactuated nature and the inability to avail comprehensive state feedback information of such ensemble systems raise significant challenges in analysis and design of ensemble systems. In this paper, we propose a moment-based ensemble control framework, which incorporates and expands the method of moments in probability theory to control theory. In particular, we establish an equivalence between ensemble systems and their moment systems in terms of control and their controllability properties by extending the Hausdorff moment problem from the perspectives of differential geometry and dynamical systems. The developments enable the design of moment-feedback control laws for closing the loop in ensemble systems using the aggregated type of measurements. The feasibility of this closed-loop control design procedure is validated both mathematically and numerically.