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The MTN predictive model is designed using a recursive approach to compensate the influence of time-delay, and an extended Kalman filter (EKF) is applied as its learning algorithm. An MTN controller is developed based on a proportional\u2013integral\u2013derivative (PID) controller where the closed-loop errors between the reference input and the system output are set as the MTN controller\u2019s inputs. Then, a back propagation (BP) algorithm, designed to update its weights according to errors caused by system uncertainty, is used as a learning algorithm for the MTN controller. Meanwhile, the convergence of the MTN predictive model and the stability of the closed-loop system are evaluated. Two numerical examples and a practical example \u2013 continuous stirred tank reactor (CSTR) process are presented to verify the superiority of the proposed scheme. The experimental results and the computational complexity analysis show that the proposed scheme is effective, promising its desirable robustness, anti-disturbance, tracking and real-time performance.<\/jats:p>","DOI":"10.1177\/01423312231180946","type":"journal-article","created":{"date-parts":[[2023,8,3]],"date-time":"2023-08-03T06:54:03Z","timestamp":1691045643000},"page":"1038-1057","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":5,"title":["Recursive\n                    <i>d<\/i>\n                    -step-ahead predictive control of MIMO nonlinear systems with input time-delay via multi-dimensional Taylor network extended from PID"],"prefix":"10.1177","volume":"46","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-5510-3152","authenticated-orcid":false,"given":"Chen-Long","family":"Li","sequence":"first","affiliation":[{"name":"Key Laboratory of Measurement and Control of Complex Systems of Engineering, Ministry of Education, Southeast University, P.R. 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