Abstract
Abstract In the present work, we develop an asymptotical control theory for a closed string under a bounded load applied to a single distinguished point. We find and describe exact classes of the string states that allows complete damping, and asymptotically exact value of the required time. We design a dry-friction like feedback control, which turns out to be asymptotically optimal. We also explicitly describe the singular arcs of the control. The central result is a proof of asymptotic optimality of the control thus constructed.
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