Asymptotic control theory for a system of linear oscillators

Aleksey Fedorov 1 Alexander Ovseevich 2

Moscow mathematical journal, 2016, 16 (3), pp.561

We present an asymptotic control theory for a system of an arbitrary number of linear oscillators under a common bounded control. We suggest a design method of a feedback control for this system. By using the DiPerna-Lions theory of singular ODEs, we prove that the suggested control law correctly defines the motion of the system. The obtained control is asymptotically optimal: the ratio of the motion time to zero under this control to the minimum one is close to 1 if the initial energy of the system is large. The results are partially based on a new perturbation theory of observable linear systems.

  • 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
  • 2. institute for Problems in Mechanics [Moscow]