{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,20]],"date-time":"2026-02-20T03:18:34Z","timestamp":1771557514540,"version":"3.50.1"},"reference-count":34,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2021,3,10]],"date-time":"2021-03-10T00:00:00Z","timestamp":1615334400000},"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":["61673141, 61806060"],"award-info":[{"award-number":["61673141, 61806060"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100005046","name":"Natural Science Foundation of Heilongjiang Province","doi-asserted-by":"publisher","award":["LH2019F024"],"award-info":[{"award-number":["LH2019F024"]}],"id":[{"id":"10.13039\/501100005046","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100010845","name":"Harbin Science and Technology Bureau","doi-asserted-by":"publisher","award":["2017RAQXJ006"],"award-info":[{"award-number":["2017RAQXJ006"]}],"id":[{"id":"10.13039\/501100010845","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100004543","name":"China Scholarship Council","doi-asserted-by":"publisher","award":["201608230319"],"award-info":[{"award-number":["201608230319"]}],"id":[{"id":"10.13039\/501100004543","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>This manuscript addresses a new multivariate generalized predictive control strategy using the least squares support vector machine for parabolic distributed parameter systems. First, a set of proper orthogonal decomposition-based spatial basis functions constructed from a carefully selected set of data is used in a Galerkin projection for the building of an approximate low-dimensional lumped parameter systems. Then, the temporal autoregressive exogenous model obtained by the least squares support vector machine is applied in the design of a multivariate generalized predictive control strategy. Finally, the effectiveness of the proposed multivariate generalized predictive control strategy is verified through a numerical simulation study on a typical diffusion-reaction process in radical symmetry.<\/jats:p>","DOI":"10.3390\/sym13030453","type":"journal-article","created":{"date-parts":[[2021,3,10]],"date-time":"2021-03-10T20:51:42Z","timestamp":1615409502000},"page":"453","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["Least Squares Support Vector Machine-Based Multivariate Generalized Predictive Control for Parabolic Distributed Parameter Systems with Control Constraints"],"prefix":"10.3390","volume":"13","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-2644-5692","authenticated-orcid":false,"given":"Ling","family":"Ai","sequence":"first","affiliation":[{"name":"Department of Automation, Harbin University of Science and Technology, Harbin 150086, China"},{"name":"Key Laboratory of Advanced Manufacturing and Intelligent Technology, Ministry of Education, Harbin University of Science and Technology, Harbin 150086, China"},{"name":"School of Electrical Engineering, Computing and Mathematical Sciences, Curtin University, Perth, WA 6845, Australia"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5219-6349","authenticated-orcid":false,"given":"Yang","family":"Xu","sequence":"additional","affiliation":[{"name":"Department of Automation, Harbin University of Science and Technology, Harbin 150086, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3996-5569","authenticated-orcid":false,"given":"Liwei","family":"Deng","sequence":"additional","affiliation":[{"name":"Key Laboratory of Advanced Manufacturing and Intelligent Technology, Ministry of Education, Harbin University of Science and Technology, Harbin 150086, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5903-7698","authenticated-orcid":false,"given":"Kok Lay","family":"Teo","sequence":"additional","affiliation":[{"name":"School of Electrical Engineering, Computing and Mathematical Sciences, Curtin University, Perth, WA 6845, Australia"},{"name":"School of Mathematical Sciences, Sunway University, Selangor 47500, Malaysia"}]}],"member":"1968","published-online":{"date-parts":[[2021,3,10]]},"reference":[{"key":"ref_1","unstructured":"Li, H.X., and Qi, C.K. 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