{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,29]],"date-time":"2026-05-29T10:39:58Z","timestamp":1780051198735,"version":"3.53.1"},"reference-count":27,"publisher":"MDPI AG","issue":"8","license":[{"start":{"date-parts":[[2023,7,30]],"date-time":"2023-07-30T00:00:00Z","timestamp":1690675200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"National Key Research and Development Plan of China","award":["2018AAA0101000"],"award-info":[{"award-number":["2018AAA0101000"]}]},{"name":"National Key Research and Development Plan of China","award":["62076028"],"award-info":[{"award-number":["62076028"]}]},{"DOI":"10.13039\/501100001809","name":"National Science Foundation of China","doi-asserted-by":"publisher","award":["2018AAA0101000"],"award-info":[{"award-number":["2018AAA0101000"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Science Foundation of China","doi-asserted-by":"publisher","award":["62076028"],"award-info":[{"award-number":["62076028"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>The model predictive control (MPC) technique is widely employed in process industries as a control scheme. The quality of the model used greatly influences the performance of the MPC. In time-varying systems, the plant model plays a critical role in determining the controller\u2019s performance, as the controller\u2019s control action relies on an adaptive model. Therefore, updating the system parameters rapidly and symmetrically in time-varying systems becomes necessary. To address this need, in the proposed work, a non-minimal state space model of a time-varying system is utilized for parameter estimation, and these parameters are updated at every sampling instant using a multi-innovation recursive least squares (MIRLS) scheme, which enables the timely updates of system parameters. We have explored various extensions of the recursive least square (RLS) scheme, such as the multi-innovation recursive least squares (MIRLS) method. This extension aims to achieve a higher convergence rate for parameter estimation. Furthermore, we have focused on the parameter estimation of a non-minimal state space time-varying system, where the system parameters change at each time interval. Additionally, we have incorporated a time-varying objective function into the MPC formulations, which enables adaptability to change the system dynamics. To demonstrate the applicability of our proposed approach, we have conducted simulation experiments using a benchmark time-varying model. These experiments showcase the effectiveness and benefits of our proposed methodology in dealing with time-varying systems.<\/jats:p>","DOI":"10.3390\/sym15081508","type":"journal-article","created":{"date-parts":[[2023,7,31]],"date-time":"2023-07-31T01:28:46Z","timestamp":1690766926000},"page":"1508","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["Adaptive Model Predictive Control Scheme Based on Non-Minimal State Space Representation"],"prefix":"10.3390","volume":"15","author":[{"given":"Zia Ur","family":"Rehman","sequence":"first","affiliation":[{"name":"State Key Laboratory of Intelligent Control and Decision of Complex Systems, School of Automation, Beijing Institute of Technology, Beijing 100081, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9862-1133","authenticated-orcid":false,"given":"Malak Abid Ali","family":"Khan","sequence":"additional","affiliation":[{"name":"State Key Laboratory of Intelligent Control and Decision of Complex Systems, School of Automation, Beijing Institute of Technology, Beijing 100081, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Hongbin","family":"Ma","sequence":"additional","affiliation":[{"name":"State Key Laboratory of Intelligent Control and Decision of Complex Systems, School of Automation, Beijing Institute of Technology, Beijing 100081, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Mizanur","family":"Rahman","sequence":"additional","affiliation":[{"name":"State Key Laboratory of Intelligent Control and Decision of Complex Systems, School of Automation, Beijing Institute of Technology, Beijing 100081, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2023,7,30]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"473","DOI":"10.1016\/j.jprocont.2013.01.004","article-title":"Performance monitoring of model-predictive controllers via model residual assessment","volume":"23","author":"Sun","year":"2013","journal-title":"J. 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