Velocity Stabilization of a Wave Equation With a Nonlinear Dynamic Boundary Condition

• 成果类型: Article
• 署名作者: Vanspranghe, Nicolas; Ferrante, Francesco; Prieur, Christophe
• 署名单位: University of Perugia; Communaute Universite Grenoble Alpes; Institut National Polytechnique de Grenoble; Universite Grenoble Alpes (UGA); Centre National de la Recherche Scientifique (CNRS)
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2021.3136086
• 发表日期: 2022
• 页码: 6786-6793
• 关键词: Distributed parameter systems; nonlinear control systems; Lyapunov methods

摘要

This article deals with a one-dimensional (1-D) wave equation with a nonlinear dynamic boundary condition and a Neumann-type boundary control acting on the other extremity. We consider a class of nonlinear stabilizing feedbacks that only depend on the velocity at the controlled extremity. The uncontrolled boundary is subject to a nonlinear first-order term, which may represent nonlinear boundary antidamping. Initial data are taken in the optimal energy space associated with the problem. Exponential decay of the mechanical energy is investigated in different cases. Stability and attractivity of suitable invariant sets are established.