文章基本信息

标题：Stabilization of the Wave Equation by the Mean of a Saturating Dirichlet Feedback
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作者：Nicolas Vanspranghe ; Francesco Ferrante ; Christophe Prieur 等
期刊名称：IFAC PapersOnLine
印刷版ISSN：2405-8963
出版年度：2021
卷号：54
期号：14
页码：442-447
DOI：10.1016/j.ifacol.2021.10.394
语种：English
出版社：Elsevier
摘要：AbstractIn this paper, we consider the wave equation with Dirichlet boundary control subject to a nonlinearity, the kind of which includes (but is not restricted to) pointwise saturation mappings. The case where only a subset of the boundary is actuated is allowed. Initial data is taken in the optimal energy space associated with Dirichlet boundary control – which means that we deal with (very) weak solutions. Using nonlinear semigroup techniques, we prove that the associated closed-loop system is asymptotically stable. Some numerical simulations are given to illustrate the stability result.
关键词：KeywordsInfinite-dimensional systemsstability of nonlinear systemscontrol of partial differential equationscontrolestimation of wave equationssystems of elasticitysemigroupoperator theory