Controllability of ensembles of linear dynamical systems

TL;DR

This paper studies how to control groups of parameter-dependent linear systems using open-loop controls, establishing conditions for controllability and revealing limitations for systems with multiple parameters.

Contribution

It provides necessary and sufficient conditions for ensemble controllability using complex approximation theory and shows that controllability is limited to systems with at most two parameters.

Findings

Ensemble controllability depends on complex approximation conditions.

Controllability holds only for systems with up to two parameters.

Applications include network synchronization and robustness analysis.

Abstract

We investigate the task of controlling ensembles of initial and terminal state vectors of parameter-dependent linear systems by applying parameter-independent open loop controls. Necessary, as well as sufficient, conditions for ensemble controllability are established, using tools from complex approximation theory. For real analytic families of linear systems it is shown that ensemble controllability holds only for systems with at most two independent parameters. We apply the results to networks of linear systems and address the question of open-loop robust synchronization.