{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,8,7]],"date-time":"2025-08-07T09:17:52Z","timestamp":1754558272728,"version":"3.37.3"},"reference-count":22,"publisher":"Oxford University Press (OUP)","issue":"3","license":[{"start":{"date-parts":[[2023,5,14]],"date-time":"2023-05-14T00:00:00Z","timestamp":1684022400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/academic.oup.com\/pages\/standard-publication-reuse-rights"}],"funder":[{"name":"Basic Research Program of Shanxi Province","award":["20210302123181"],"award-info":[{"award-number":["20210302123181"]}]},{"DOI":"10.13039\/501100002858","name":"China Postdoctoral Science Foundation","doi-asserted-by":"publisher","award":["2020M680919"],"award-info":[{"award-number":["2020M680919"]}],"id":[{"id":"10.13039\/501100002858","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2023,9,20]]},"abstract":"<jats:title>Abstract<\/jats:title>\n               <jats:p>In this paper, we are concerned with adaptive stabilization for a wave equation subject to boundary control matched harmonic disturbance. We use the adaptive and Lyapunov approach to estimate unknown disturbance and construct an adaptive boundary feedback controller. By the semigroup theory and Lasalle\u2018s invariance theorem, the well-posedness and asymptotic stability of the closed-loop system is proved, respectively. At the same time, it is shown that the parameter estimates involved in the constructed controller converge to their own real values as time goes to infinity. Some numerical simulations are offered at the end of the paper to illustrate the effectiveness of theoretical results.<\/jats:p>","DOI":"10.1093\/imamci\/dnad010","type":"journal-article","created":{"date-parts":[[2023,5,16]],"date-time":"2023-05-16T14:01:56Z","timestamp":1684245716000},"page":"429-444","source":"Crossref","is-referenced-by-count":1,"title":["Adaptive stabilization for a wave equation subject to boundary control matched harmonic disturbance"],"prefix":"10.1093","volume":"40","author":[{"given":"Jun-Jun","family":"Liu","sequence":"first","affiliation":[{"name":"College of Mathematics , Taiyuan University of Technology, Taiyuan 030024 , China"}]},{"given":"Yan-Xing","family":"Zhao","sequence":"additional","affiliation":[{"name":"College of Mathematics , Taiyuan University of Technology, Taiyuan 030024 , China"}]}],"member":"286","published-online":{"date-parts":[[2023,5,14]]},"reference":[{"article-title":"A frequency approach for stabilization of one-dimensional degenerate wave equation","year":"2018","author":"Aissa","key":"2023092216573145800_ref1"},{"key":"2023092216573145800_ref2","doi-asserted-by":"crossref","first-page":"2052","DOI":"10.1137\/15M1020538","article-title":"Control and stabilization of degenerate wave equation","volume":"55","author":"Alabau-Boussouira","year":"2017","journal-title":"SIAM J. Control Optim."},{"key":"2023092216573145800_ref3","doi-asserted-by":"crossref","DOI":"10.1016\/j.aml.2021.107235","article-title":"Exact controllability for a one-dimensional degenerate wave equation in domains with moving boundary","volume":"119","author":"Bai","year":"2021","journal-title":"Appl. Math. Lett."},{"key":"2023092216573145800_ref4","doi-asserted-by":"crossref","first-page":"6045","DOI":"10.2298\/FIL1817045B","article-title":"Energy decay for a degenerate wave equation under fractional derivative controls","volume":"32","author":"Benaissa","year":"2018","journal-title":"Filomat"},{"key":"2023092216573145800_ref5","first-page":"125","article-title":"A degenerate parabolic equation arising in image processing","volume":"8","author":"Citti","year":"2004","journal-title":"Commun. Appl. Anal."},{"key":"2023092216573145800_ref6","doi-asserted-by":"crossref","first-page":"360","DOI":"10.1016\/j.automatica.2018.11.033","article-title":"Output regulation for coupled linear parabolic PIDEs","volume":"100","author":"Deutscher","year":"2019","journal-title":"Automatica J. IFAC"},{"key":"2023092216573145800_ref7","doi-asserted-by":"crossref","first-page":"483","DOI":"10.1002\/cpa.3160290503","article-title":"A class of degenerate diffusion processes occurring in population genetics","volume":"29","author":"Ethier","year":"1976","journal-title":"Commun. Pure Appl. Math."},{"key":"2023092216573145800_ref8","doi-asserted-by":"crossref","first-page":"2017","DOI":"10.1002\/asjc.2104","article-title":"Backstepping design for a class of coupled parabolic PDEs with spatially varying coefficient","volume":"22","author":"Ghaderi","year":"2020","journal-title":"Asian J. Control."},{"key":"2023092216573145800_ref9","doi-asserted-by":"crossref","first-page":"3","DOI":"10.1175\/1520-0469(1976)033<0003:CSFAST>2.0.CO;2","article-title":"Climate stability for a sellers type model","volume":"33","author":"Ghil","year":"1976","journal-title":"J. Atmos. Sci."},{"key":"2023092216573145800_ref10","doi-asserted-by":"crossref","first-page":"3","DOI":"10.1137\/080716827","article-title":"Cloaking devices, electromagnetic wormholes, and transformation optics","volume":"51","author":"Greenleaf","year":"2009","journal-title":"SIAM Rev."},{"key":"2023092216573145800_ref11","doi-asserted-by":"crossref","first-page":"1679","DOI":"10.1137\/120873212","article-title":"Adaptive output feedback stabilization for one-dimensional wave equation with corrupted observation by harmonic disturbance","volume":"51","author":"Guo","year":"2013","journal-title":"SIAM J. Control Optim."},{"key":"2023092216573145800_ref12","doi-asserted-by":"crossref","first-page":"514","DOI":"10.1002\/rnc.1843","article-title":"Stabilization and regulator design for a one-dimensional unstable wave equation with input harmonic disturbance","volume":"23","author":"Guo","year":"2013","journal-title":"Int. J. Robust Nonlinear Control"},{"key":"2023092216573145800_ref13","doi-asserted-by":"crossref","first-page":"1631","DOI":"10.1109\/TAC.2013.2239003","article-title":"Parameter estimation and non-collocated adaptive stabilization for a wave equation subject to general boundary harmonic disturbance, IEEE trans","volume":"58","author":"Guo","year":"2013","journal-title":"Autom. Control."},{"key":"2023092216573145800_ref14","doi-asserted-by":"crossref","first-page":"2194","DOI":"10.1002\/rnc.2977","article-title":"Sliding mode control and active disturbance rejection control to the stabilization of one-dimensional Schr\u00f6dinger equation subject to boundary control matched disturbance","volume":"24","author":"Guo","year":"2014","journal-title":"Int. J. Robust Nonlinear Control"},{"key":"2023092216573145800_ref15","doi-asserted-by":"crossref","first-page":"381","DOI":"10.1080\/00207179.2011.557092","article-title":"Parameter estimation and stabilisation for a one-dimensional wave equation with boundary output constant disturbance and non-collocated control","volume":"84","author":"Guo","year":"2011","journal-title":"Int. J. Control"},{"key":"2023092216573145800_ref16","doi-asserted-by":"crossref","first-page":"68","DOI":"10.1137\/0321004","article-title":"Control of wave processes with distributed controls supported on a subregion","volume":"21","author":"Lagnese","year":"1983","journal-title":"SIAM J. Control Optim."},{"key":"2023092216573145800_ref17","doi-asserted-by":"crossref","first-page":"1120","DOI":"10.1109\/TAC.2021.3056599","article-title":"Robust tracking error feedback control for a one-dimensional Schr\u00f6dinger equation, IEEE trans","volume":"67","author":"Liu","year":"2022","journal-title":"Autom. Control."},{"key":"2023092216573145800_ref18","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4471-0419-3","volume-title":"Stability and Stabilization of Infinite Dimensional Systems with Applications","author":"Luo","year":"1999"},{"volume-title":"Boundary stabilization of numerical approximations of the 1-d variable coefficients wave equation: A numerical viscosity approach","year":"2014","author":"Marica","key":"2023092216573145800_ref19"},{"volume-title":"M. A. Naimark, Linear Differential Operators","year":"1967","author":"Naimark","key":"2023092216573145800_ref20"},{"key":"2023092216573145800_ref21","doi-asserted-by":"crossref","DOI":"10.1016\/j.sysconle.2020.104780","article-title":"Output feedback stabilization for 1-D wave equation with variable coefficients and non-collocated observation","volume":"145","author":"Wu","year":"2020","journal-title":"Syst. Control Lett."},{"key":"2023092216573145800_ref24","doi-asserted-by":"crossref","first-page":"6003","DOI":"10.1109\/TAC.2021.3058905","article-title":"Boundary control and observation to inverse coefficient problem for heat equation with unknown source and initial value","volume":"66","author":"Zhao","year":"2021","journal-title":"IEEE Trans. Autom. Control."}],"container-title":["IMA Journal of Mathematical Control and Information"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/academic.oup.com\/imamci\/article-pdf\/40\/3\/429\/51714030\/dnad010.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"syndication"},{"URL":"https:\/\/academic.oup.com\/imamci\/article-pdf\/40\/3\/429\/51714030\/dnad010.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,9,22]],"date-time":"2023-09-22T17:23:40Z","timestamp":1695403420000},"score":1,"resource":{"primary":{"URL":"https:\/\/academic.oup.com\/imamci\/article\/40\/3\/429\/7161853"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,5,14]]},"references-count":22,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2023,5,14]]},"published-print":{"date-parts":[[2023,9,20]]}},"URL":"https:\/\/doi.org\/10.1093\/imamci\/dnad010","relation":{},"ISSN":["0265-0754","1471-6887"],"issn-type":[{"type":"print","value":"0265-0754"},{"type":"electronic","value":"1471-6887"}],"subject":[],"published-other":{"date-parts":[[2023,9]]},"published":{"date-parts":[[2023,5,14]]}}}