{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,30]],"date-time":"2025-10-30T07:10:02Z","timestamp":1761808202363,"version":"build-2065373602"},"reference-count":45,"publisher":"MDPI AG","issue":"6","license":[{"start":{"date-parts":[[2018,6,14]],"date-time":"2018-06-14T00:00:00Z","timestamp":1528934400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["61573298"],"award-info":[{"award-number":["61573298"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Algorithms"],"abstract":"<jats:p>This paper presents a second order P-type iterative learning control (ILC) scheme with initial state learning for a class of fractional order linear distributed parameter systems. First, by analyzing the control and learning processes, a discrete system for P-type ILC is established, and the ILC design problem is then converted to a stability problem for such a discrete system. Next, a sufficient condition for the convergence of the control input and the tracking errors is obtained by introducing a new norm and using the generalized Gronwall inequality, which is less conservative than the existing one. Finally, the validity of the proposed method is verified by a numerical example.<\/jats:p>","DOI":"10.3390\/a11060085","type":"journal-article","created":{"date-parts":[[2018,6,14]],"date-time":"2018-06-14T11:06:06Z","timestamp":1528974366000},"page":"85","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["ILC with Initial State Learning for Fractional Order Linear Distributed Parameter Systems"],"prefix":"10.3390","volume":"11","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-7072-4798","authenticated-orcid":false,"given":"Yong-Hong","family":"Lan","sequence":"first","affiliation":[{"name":"School of Information Engineering, Xiangtan University, Xiangtan 411105, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zhe-Min","family":"Cui","sequence":"additional","affiliation":[{"name":"School of Information Engineering, Xiangtan University, Xiangtan 411105, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2018,6,14]]},"reference":[{"key":"ref_1","unstructured":"Xu, J.X., and Tan, Y. 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