Controlling Multiparticle System on a Line. I

TL;DR

This paper investigates the controllability and control properties of a classical multiparticle system, like the Toda lattice, focusing on nonperiodic configurations and employing geometric control theory methods.

Contribution

It provides complete and partial answers to control-related questions for nonperiodic multiparticle systems, advancing geometric control techniques.

Findings

Criteria for controllability established

Methods for feedback linearization developed

Insights into time-optimal particle relocation

Abstract

We study a classical multiparticle system (such as Toda lattice) whose dynamics we intend to control by forces applied to few particles of the system. Various problem settings, typical for control theory are posed for this model; among those: studying accessibility and controllability properties, structure properties and feedback linearization of respective control system, time-optimal relocation of particles. We obtain complete or partial answers to the posed questions; criteria and methods of geometric control theory are employed. In the present part I we consider nonperiodic multiparticle system. In the forthcoming Part II we address controllability issue for multiparticle system subject to periodic boundary conditions. That study would require an extension and refinement of known methods of geometric control.