{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,17]],"date-time":"2025-12-17T08:49:18Z","timestamp":1765961358785,"version":"3.41.2"},"reference-count":52,"publisher":"Wiley","issue":"1","license":[{"start":{"date-parts":[[2021,3,31]],"date-time":"2021-03-31T00:00:00Z","timestamp":1617148800000},"content-version":"vor","delay-in-days":89,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["51875457","61903298"],"award-info":[{"award-number":["51875457","61903298"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["Complexity"],"published-print":{"date-parts":[[2021,1]]},"abstract":"<jats:p>A model predictive control (MPC) method based on recursive backpropagation (RBP) neural network and genetic algorithm (GA) is proposed for a class of nonlinear systems with time delays and uncertainties. In the offline modeling stage, a multistep\u2010ahead predictor with GA\u2010RBP neural network is designed, where GA\u2010BP neural network is used as a one\u2010step prediction model and GA is employed to train the initial weights and bias of the BP neural network. The incorporation of GA into RBP can reduce the possibility of the BP neural network falling into a local optimum instead of reaching global optimization. In the online optimizing stage, a multistep\u2010ahead GA\u2010RBP neural network predictor and an improved gradient descent method (IGDM) are proposed to efficiently solve the online optimization problem of nonlinear MPC by minimizing a modified quadratic criterion. The designed MPC strategy can avoid information loss while linearizing the controlled system and computing the Hessian matrix and its inverse matrix. Experimental results show that the proposed approach can reduce the computational burden and improve the performance of MPC (i.e., the maximum overshoots, calculation time, rise time, and RMSE tracking error value) for the solution of nonlinear controlled systems.<\/jats:p>","DOI":"10.1155\/2021\/6622149","type":"journal-article","created":{"date-parts":[[2021,3,31]],"date-time":"2021-03-31T19:20:08Z","timestamp":1617218408000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":11,"title":["Model Predictive Control of Nonlinear System Based on GA\u2010RBP Neural Network and Improved Gradient Descent Method"],"prefix":"10.1155","volume":"2021","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-5184-2705","authenticated-orcid":false,"given":"Youming","family":"Wang","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0202-7069","authenticated-orcid":false,"given":"Didi","family":"Qing","sequence":"additional","affiliation":[]}],"member":"311","published-online":{"date-parts":[[2021,3,31]]},"reference":[{"key":"e_1_2_10_1_2","doi-asserted-by":"publisher","DOI":"10.1109\/TCST.2011.2124461"},{"key":"e_1_2_10_2_2","doi-asserted-by":"publisher","DOI":"10.1109\/tie.2007.896492"},{"key":"e_1_2_10_3_2","doi-asserted-by":"publisher","DOI":"10.1109\/tie.2010.2041733"},{"key":"e_1_2_10_4_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.isatra.2019.08.001"},{"key":"e_1_2_10_5_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.conengprac.2015.09.005"},{"key":"e_1_2_10_6_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.jprocont.2014.12.003"},{"key":"e_1_2_10_7_2","doi-asserted-by":"publisher","DOI":"10.1109\/TCST.2006.883339"},{"key":"e_1_2_10_8_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.conengprac.2012.01.001"},{"key":"e_1_2_10_9_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.enbuild.2017.02.012"},{"key":"e_1_2_10_10_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.cej.2020.126673"},{"key":"e_1_2_10_11_2","doi-asserted-by":"publisher","DOI":"10.1109\/91.855918"},{"key":"e_1_2_10_12_2","doi-asserted-by":"publisher","DOI":"10.1016\/S0098-1354(96)00279-7"},{"key":"e_1_2_10_13_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.automatica.2006.02.023"},{"key":"e_1_2_10_14_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.jprocont.2013.01.007"},{"key":"e_1_2_10_15_2","first-page":"247","article-title":"Nonlinear predictive control based on artificial neural networks","volume":"14","author":"Spisiak M.","year":"2004","journal-title":"Neural Network World"},{"key":"e_1_2_10_16_2","doi-asserted-by":"publisher","DOI":"10.1109\/tnnls.2015.2411671"},{"key":"e_1_2_10_17_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.isatra.2017.10.011"},{"key":"e_1_2_10_18_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.asoc.2010.07.021"},{"key":"e_1_2_10_19_2","doi-asserted-by":"publisher","DOI":"10.1007\/bf02551274"},{"key":"e_1_2_10_20_2","doi-asserted-by":"publisher","DOI":"10.1016\/0893-6080(89)90003-8"},{"key":"e_1_2_10_21_2","doi-asserted-by":"publisher","DOI":"10.1016\/0893-6080(89)90020-8"},{"key":"e_1_2_10_22_2","doi-asserted-by":"publisher","DOI":"10.1109\/TNNLS.2013.2261574"},{"key":"e_1_2_10_23_2","doi-asserted-by":"crossref","unstructured":"\u0141awry\u0144czukM. Computationally efficient nonlinear predictive control based on RBF neural multi-models Proceedings of the International Conference on Adaptive & Natural Computing Algorithms April 2009 Berlin Heidelberg Springer-Verlag.","DOI":"10.1007\/978-3-642-04921-7_10"},{"key":"e_1_2_10_24_2","doi-asserted-by":"publisher","DOI":"10.1515\/acsc-2016-0007"},{"key":"e_1_2_10_25_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.jpowsour.2007.12.036"},{"key":"e_1_2_10_26_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.autcon.2019.102928"},{"key":"e_1_2_10_27_2","doi-asserted-by":"crossref","unstructured":"SudibyoM. M. N.andAzizN. MIMO Neural Wiener based Model Predictive Control (NWMPC) for MTBE reactive distillation using simulated annealing-particle swarm optimization (SA-PSO) Proceedings of 12th International Symposium on Process Systems Engineering and 25th European Symposium on Computer Aided Process Engineering May 2015 Copenhagen Denmark 1631\u20131636 https:\/\/doi.org\/10.1016\/b978-0-444-63577-8.50117-0 2-s2.0-84940501206.","DOI":"10.1016\/B978-0-444-63577-8.50117-0"},{"key":"e_1_2_10_28_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.compstruct.2019.111739"},{"key":"e_1_2_10_29_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.ast.2010.01.005"},{"key":"e_1_2_10_30_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.cogsys.2020.12.006"},{"key":"e_1_2_10_31_2","doi-asserted-by":"publisher","DOI":"10.1007\/s00340-020-07455-y"},{"key":"e_1_2_10_32_2","doi-asserted-by":"publisher","DOI":"10.1016\/s1474-6670(17)34807-3"},{"key":"e_1_2_10_33_2","doi-asserted-by":"publisher","DOI":"10.1109\/TIE.2009.2025714"},{"key":"e_1_2_10_34_2","doi-asserted-by":"publisher","DOI":"10.1109\/TAC.2011.2176389"},{"key":"e_1_2_10_35_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.jprocont.2008.09.003"},{"key":"e_1_2_10_36_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.oceaneng.2020.107885"},{"key":"e_1_2_10_37_2","doi-asserted-by":"publisher","DOI":"10.1080\/0020718508961129"},{"key":"e_1_2_10_38_2","doi-asserted-by":"crossref","unstructured":"BaiL.andCocaD. Nonlinear predictive control based on NARMAX models Proceedings of the International Conference on Optimization of Electrical & Electronic Equipment May 2008 Brasov Romania IEEE.","DOI":"10.1109\/OPTIM.2008.4602450"},{"key":"e_1_2_10_39_2","doi-asserted-by":"publisher","DOI":"10.1007\/3-540-49430-8_3"},{"key":"e_1_2_10_40_2","first-page":"281","article-title":"Random search for hyper-parameter optimization","volume":"13","author":"Bergstra J.","year":"2012","journal-title":"Journal of Machine Learning Research"},{"key":"e_1_2_10_41_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcsr.2020.106443"},{"key":"e_1_2_10_42_2","doi-asserted-by":"publisher","DOI":"10.1021\/ie8008633"},{"key":"e_1_2_10_43_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.renene.2016.03.103"},{"key":"e_1_2_10_44_2","doi-asserted-by":"publisher","DOI":"10.1109\/4235.771166"},{"key":"e_1_2_10_45_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.compchemeng.2005.08.005"},{"key":"e_1_2_10_46_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.ces.2007.03.042"},{"key":"e_1_2_10_47_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.isatra.2009.06.002"},{"key":"e_1_2_10_48_2","doi-asserted-by":"publisher","DOI":"10.1016\/s0098-1354(01)00715-3"},{"key":"e_1_2_10_49_2","doi-asserted-by":"publisher","DOI":"10.1109\/9.847117"},{"key":"e_1_2_10_50_2","doi-asserted-by":"publisher","DOI":"10.1109\/TAC.2003.819287"},{"key":"e_1_2_10_51_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.procs.2017.11.325"},{"key":"e_1_2_10_52_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.engappai.2017.07.011"}],"container-title":["Complexity"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/downloads.hindawi.com\/journals\/complexity\/2021\/6622149.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/complexity\/2021\/6622149.xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1155\/2021\/6622149","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,8,9]],"date-time":"2024-08-09T21:31:08Z","timestamp":1723239068000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1155\/2021\/6622149"}},"subtitle":[],"editor":[{"given":"Thach Ngoc","family":"Dinh","sequence":"additional","affiliation":[]}],"short-title":[],"issued":{"date-parts":[[2021,1]]},"references-count":52,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2021,1]]}},"alternative-id":["10.1155\/2021\/6622149"],"URL":"https:\/\/doi.org\/10.1155\/2021\/6622149","archive":["Portico"],"relation":{},"ISSN":["1076-2787","1099-0526"],"issn-type":[{"type":"print","value":"1076-2787"},{"type":"electronic","value":"1099-0526"}],"subject":[],"published":{"date-parts":[[2021,1]]},"assertion":[{"value":"2020-12-01","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"2021-03-23","order":2,"name":"accepted","label":"Accepted","group":{"name":"publication_history","label":"Publication History"}},{"value":"2021-03-31","order":3,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}],"article-number":"6622149"}}