Controlling multiparticle system on the line. I

We study classical multiparticle system (e.g. Toda lattice) on the line whose dynamics will be controlled 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.