Global asymptotic stabilization of the Hunter-Saxton control system

In this paper, the asymptotic stabilization problem of the Hunter-Saxton equation in the periodic setting is solved. We first design feedback control law, and distinguish the controlled state into favorable situa-tion and unfavourable situation. Then, we establish the local well-posedness for the closed-loop control system by the means of a fixed-point scheme of Schauder's type. We also present some energy estimates with respect to two situations. Finally, by introducing a Lyapunov functional, we obtain global asymptotic stabilization result for the control problem of Hunter-Saxton equation. (c) 2021 European Control Association. Published by Elsevier Ltd. All rights reserved.