Elements of asymptotic control theory for a closed string
We study the asymptotical control theory for one of the simplest distributed oscillating system --- the closed string
under a bounded load applied to a single distinguished point. We find exact classes of the string states that allows
complete damping, and asymptotically exact value of the required time. We specify the structure of the asymptotically
optimal feedback control, which is dry-friction like. The motion under the control is described via a nonlinear wave equation. We prove the related existence and uniqueness results. We also prove the asymptotic optimality of the control.