On Uniform Ensemble Controllability of Diagonalizable Linear Ensemble Systems

TL;DR

This paper develops an algebraic framework using the Stone-Weierstrass theorem to analyze uniform ensemble controllability of diagonalizable linear systems, introducing a controllability matrix with a rank condition as a key criterion.

Contribution

It introduces a novel algebraic approach and controllability matrix for assessing UEC in linear ensemble systems, extending existing results and addressing new cases.

Findings

The controllability matrix's rank condition is necessary and sufficient for UEC.

The framework encompasses and generalizes previous results.

Examples demonstrate the effectiveness of the proposed approach.

Abstract

In this paper, we study uniform ensemble controllability (UEC) of linear ensemble systems defined in an infinite-dimensional space through finite-dimensional settings. Specifically, with the help of the Stone-Weierstrass theorem for modules, we provide an algebraic framework for examining UEC of linear ensemble systems with diagonalizable drift vector fields through checking the controllability of finite-dimensional subsystems in the ensemble. The new framework renders a novel concept of ensemble controllability matrix, which rank-condition serves as a sufficient and necessary condition for UEC of linear ensembles. We provide several examples demonstrating that the proposed approach well-encompasses existing results and analyzes UEC of linear ensembles not addressed by literature.