Asymptotically optimal control for a simplest distributed system

Alexander Ovseevich 1 Aleksey Fedorov 2

Доклады Академии Наук / Doklady Mathematics, MAIK Nauka/Interperiodica, 2017, 95 (2), pp.194 - 197

We study the problem of the minimum-time damping of a closed string under a bounded load, applied at a single fixed point. A constructive feedback control law is designed, which allows bringing the system to a bounded neighbourhood of the terminal manifold. The law has the form of the dry friction at the point, where the load is applied. The motion under the control is governed by a nonlinear wave equation. The existence and uniqueness of solution of the Cauchy problem for this equation are proved. The main result is the asymptotic optimality of the suggested control law.

  • 1. Institute for Problems in Mechanics of Russian Academy of Sciences
  • 2. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques