{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T12:37:36Z","timestamp":1740141456557,"version":"3.37.3"},"reference-count":22,"publisher":"Oxford University Press (OUP)","issue":"4","license":[{"start":{"date-parts":[[2020,8,13]],"date-time":"2020-08-13T00:00:00Z","timestamp":1597276800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/academic.oup.com\/journals\/pages\/open_access\/funder_policies\/chorus\/standard_publication_model"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["61873153"],"award-info":[{"award-number":["61873153"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2020,12,16]]},"abstract":"<jats:title>Abstract<\/jats:title>\n               <jats:p>In this paper, we consider output tracking for a one-dimensional wave equation, where the boundary disturbances are either collocated or non-collocated with control. The regulated output and the control are supposed to be non-collocated with control, which represents a difficult case for output tracking of PDEs. We apply the trajectory planning approach to design an observer, in terms of tracking error only, to estimate both states of the system and the exosystem from which the disturbances are produced. An error-based feedback control is proposed by solving a standard regulator equation. It is shown that (a) the closed-loop system is uniformly bounded whenever the exosystem is bounded; (b) when the disturbance is zero, the closed-loop is asymptotically stable; and (c) the tracking error converges to zero asymptotically as time goes to infinity. Numerical simulations are performed to validate the effectiveness of the proposed control.<\/jats:p>","DOI":"10.1093\/imamci\/dnaa020","type":"journal-article","created":{"date-parts":[[2020,7,24]],"date-time":"2020-07-24T19:13:34Z","timestamp":1595618014000},"page":"1447-1467","source":"Crossref","is-referenced-by-count":1,"title":["Error-based output tracking for a one-dimensional wave equation with harmonic type disturbance"],"prefix":"10.1093","volume":"37","author":[{"given":"Ziqing","family":"Tian","sequence":"first","affiliation":[{"name":"Department of Economics, University of Michigan, Ann Arbor, MI 48104, USA"}]},{"given":"Xiao-Hui","family":"Wu","sequence":"additional","affiliation":[{"name":"School of Mathematical Sciences, Shanxi University, Taiyuan, Shanxi 030006, China"}]}],"member":"286","published-online":{"date-parts":[[2020,8,13]]},"reference":[{"key":"2020121600435388900_ref1","doi-asserted-by":"crossref","first-page":"25","DOI":"10.1109\/TAC.1976.1101137","article-title":"The robust control of a servomechanism problem for linear time-invariant multivariable systems","volume":"21","author":"Davison","year":"1976","journal-title":"IEEE Trans. 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