Ensemble controllability by Lie algebraic methods

TL;DR

This paper investigates the controllability of parameterized families of nonlinear control systems using Lie algebraic techniques, establishing conditions for exact and approximate controllability of ensembles.

Contribution

It introduces new Lie algebraic methods to analyze ensemble controllability, proving genericity of exact controllability and providing approximate controllability criteria.

Findings

Genericity of exact controllability for finite ensembles

Sufficient approximate controllability condition in $ ext{R}^3$

A variant of Rashevsky-Chow theorem for control-linear ensembles

Abstract

We study possibilities to control an ensemble (a parameterized family) of nonlinear control systems by a single parameter-independent control. Proceeding by Lie algebraic methods we establish genericity of exact controllability property for finite ensembles, prove sufficient approximate controllability condition for a model problem in $\mathbb{R}^3$, and provide a variant of Rashevsky-Chow theorem for approximate controllability of control-linear ensembles.