{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,17]],"date-time":"2026-04-17T16:41:13Z","timestamp":1776444073112,"version":"3.51.2"},"reference-count":54,"publisher":"Institute of Electrical and Electronics Engineers (IEEE)","license":[{"start":{"date-parts":[[2025,1,1]],"date-time":"2025-01-01T00:00:00Z","timestamp":1735689600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by-nc-nd\/4.0\/"}],"funder":[{"name":"European Union\u2019s Horizon 2020 Research and Innovation Programme","award":["953348"],"award-info":[{"award-number":["953348"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["IEEE Trans. Automat. Sci. Eng."],"published-print":{"date-parts":[[2025]]},"DOI":"10.1109\/tase.2024.3479321","type":"journal-article","created":{"date-parts":[[2024,10,22]],"date-time":"2024-10-22T17:31:15Z","timestamp":1729618275000},"page":"8137-8149","source":"Crossref","is-referenced-by-count":8,"title":["Learning Control Affine Neural NARX Models for Internal Model Control Design"],"prefix":"10.1109","volume":"22","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-2791-370X","authenticated-orcid":false,"given":"Jing","family":"Xie","sequence":"first","affiliation":[{"name":"Dipartimento di Elettronica Informazione e Bioingegneria, Politecnico di Milano, Milan, Italy"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7270-8185","authenticated-orcid":false,"given":"Fabio","family":"Bonassi","sequence":"additional","affiliation":[{"name":"Department of Information Technology, Uppsala University, Uppsala, Sweden"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1804-9921","authenticated-orcid":false,"given":"Riccardo","family":"Scattolini","sequence":"additional","affiliation":[{"name":"Dipartimento di Elettronica Informazione e Bioingegneria, Politecnico di Milano, Milan, Italy"}]}],"member":"263","reference":[{"key":"ref1","doi-asserted-by":"publisher","DOI":"10.1146\/annurev-control-030323-024328"},{"key":"ref2","doi-asserted-by":"publisher","DOI":"10.1109\/TCST.2019.2949757"},{"key":"ref3","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-030-35713-9","volume-title":"Koopman Operator in Systems and Control","author":"Mauroy","year":"2020"},{"key":"ref4","doi-asserted-by":"crossref","first-page":"92","DOI":"10.1016\/j.jprocont.2022.04.011","article-title":"On recurrent neural networks for learning-based control: Recent results and ideas for future developments","volume":"114","author":"Bonassi","year":"2022","journal-title":"J. Process Control"},{"key":"ref5","doi-asserted-by":"publisher","DOI":"10.1109\/TNNLS.2021.3107600"},{"key":"ref6","doi-asserted-by":"publisher","DOI":"10.1016\/j.neucom.2021.01.096"},{"key":"ref7","doi-asserted-by":"publisher","DOI":"10.1109\/TFUZZ.2022.3217378"},{"key":"ref8","doi-asserted-by":"publisher","DOI":"10.1109\/TCYB.2023.3255925"},{"key":"ref9","doi-asserted-by":"publisher","DOI":"10.1109\/TFUZZ.2021.3089031"},{"issue":"2","key":"ref10","doi-asserted-by":"crossref","first-page":"308","DOI":"10.1021\/i200017a016","article-title":"Internal model control. A unifying review and some new results","volume":"21","author":"Garcia","year":"1982","journal-title":"Ind. Eng. Chem. Process Design Develop."},{"key":"ref11","doi-asserted-by":"publisher","DOI":"10.4103\/0256-4602.105001"},{"issue":"2","key":"ref12","doi-asserted-by":"crossref","first-page":"403","DOI":"10.1021\/i200033a010","article-title":"Internal model control: Extension to nonlinear system","volume":"25","author":"Economou","year":"1986","journal-title":"Ind. Eng. Chem. Process Design Develop."},{"key":"ref13","doi-asserted-by":"publisher","DOI":"10.1007\/978-0-85729-398-5_7"},{"issue":"6","key":"ref14","doi-asserted-by":"crossref","first-page":"789","DOI":"10.1016\/S0005-1098(99)00214-9","article-title":"Constrained model predictive control: Stability and optimality","volume":"36","author":"Mayne","year":"2000","journal-title":"Automatica"},{"key":"ref15","volume":"2","author":"Rawlings","year":"2017","journal-title":"Model Predictive Control: Theory, Computation, and Design"},{"key":"ref16","doi-asserted-by":"publisher","DOI":"10.4249\/scholarpedia.2330"},{"key":"ref17","article-title":"Empirical evaluation of gated recurrent neural networks on sequence modeling","author":"Chung","year":"2014","journal-title":"arXiv:1412.3555"},{"key":"ref18","doi-asserted-by":"publisher","DOI":"10.1162\/neco.1997.9.8.1735"},{"key":"ref19","doi-asserted-by":"crossref","DOI":"10.1016\/j.automatica.2023.111472","article-title":"Robust constrained nonlinear model predictive control with gated recurrent unit model","volume":"161","author":"Schimperna","year":"2024","journal-title":"Automatica"},{"key":"ref20","doi-asserted-by":"publisher","DOI":"10.1109\/72.478390"},{"key":"ref21","doi-asserted-by":"publisher","DOI":"10.1016\/S0005-1098(01)00028-0"},{"key":"ref22","doi-asserted-by":"publisher","DOI":"10.23919\/ECC.2013.6669322"},{"key":"ref23","doi-asserted-by":"publisher","DOI":"10.1002\/aic.17013"},{"key":"ref24","first-page":"2123","article-title":"An offset-free nonlinear MPC scheme for systems learned by neural NARX models","volume-title":"Proc. IEEE 61st Conf. Decis. Control (CDC)","author":"Bonassi"},{"issue":"16","key":"ref25","doi-asserted-by":"crossref","first-page":"9992","DOI":"10.1002\/rnc.6883","article-title":"Robust offset-free nonlinear model predictive control for systems learned by neural nonlinear autoregressive exogenous models","volume":"33","author":"Xie","year":"2023","journal-title":"Int. J. Robust Nonlinear Control"},{"issue":"14","key":"ref26","first-page":"54","article-title":"Nonlinear MPC for offset-free tracking of systems learned by gru neural networks","volume-title":"Proc. 3rd IFAC Conf. Model., Identificat. Control Nonlinear Syst. (MICNON)","volume":"54","author":"Bonassi"},{"issue":"18","key":"ref27","doi-asserted-by":"crossref","first-page":"8877","DOI":"10.1002\/rnc.5519","article-title":"Learning model predictive control with long short-term memory networks","volume":"31","author":"Terzi","year":"2021","journal-title":"Int. J. Robust Nonlinear Control"},{"issue":"1","key":"ref28","doi-asserted-by":"crossref","first-page":"156","DOI":"10.1016\/j.ifacol.2023.02.027","article-title":"On offset-free model predictive control with long short-term memory networks","volume":"56","author":"Schimperna","year":"2023","journal-title":"IFAC-PapersOnLine"},{"key":"ref29","doi-asserted-by":"publisher","DOI":"10.1145\/3514228"},{"key":"ref30","doi-asserted-by":"crossref","DOI":"10.1016\/j.jprocont.2023.103005","article-title":"Physics-informed recurrent neural network modeling for predictive control of nonlinear processes","volume":"128","author":"Zheng","year":"2023","journal-title":"J. Process Control"},{"key":"ref31","doi-asserted-by":"publisher","DOI":"10.1016\/j.jprocont.2020.03.013"},{"key":"ref32","doi-asserted-by":"publisher","DOI":"10.1109\/TCST.2024.3355476"},{"key":"ref33","doi-asserted-by":"crossref","DOI":"10.1007\/BFb0006368","volume-title":"Nonlinear Control Systems: An Introduction","author":"Isidori","year":"1985"},{"key":"ref34","doi-asserted-by":"crossref","first-page":"375","DOI":"10.1016\/B978-0-12-817582-8.00022-2","article-title":"Single-link flexible joint manipulator control using backstepping technique","volume-title":"Backstepping Control of Nonlinear Dynamical Systems","author":"Bansal","year":"2021"},{"key":"ref35","doi-asserted-by":"publisher","DOI":"10.1109\/ACCESS.2020.3003167"},{"issue":"10","key":"ref36","doi-asserted-by":"crossref","first-page":"6176","DOI":"10.1109\/TAC.2023.3293025","article-title":"A time-varying observer-based approach to equilibrium estimation and compensation for synchronization of heterogeneous nonlinear cyber-physical systems","volume":"68","author":"Wang","year":"2023","journal-title":"IEEE Trans. Autom. Control"},{"key":"ref37","doi-asserted-by":"publisher","DOI":"10.1109\/TAC.2022.3143082"},{"key":"ref38","doi-asserted-by":"publisher","DOI":"10.1109\/ACCESS.2019.2923658"},{"key":"ref39","doi-asserted-by":"publisher","DOI":"10.23919\/ACC53348.2022.9867266"},{"key":"ref40","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-031-51500-2_7"},{"issue":"5","key":"ref41","doi-asserted-by":"crossref","first-page":"431","DOI":"10.1049\/ip-d.1991.0059","article-title":"Neural networks for nonlinear internal model control","volume":"138","author":"Hunt","year":"1991","journal-title":"IEE Proc. D, Control Theory Appl."},{"key":"ref42","doi-asserted-by":"publisher","DOI":"10.1109\/72.822512"},{"key":"ref43","doi-asserted-by":"publisher","DOI":"10.1109\/87.845876"},{"issue":"5","key":"ref44","doi-asserted-by":"crossref","first-page":"800","DOI":"10.1016\/j.jprocont.2011.03.003","article-title":"A comparative analysis of distributed MPC techniques applied to the HD-MPC four-tank benchmark","volume":"21","author":"Alvarado","year":"2011","journal-title":"J. Process Control"},{"issue":"7","key":"ref45","doi-asserted-by":"crossref","first-page":"547","DOI":"10.1016\/j.ifacol.2021.08.417","article-title":"Stability of discrete-time feed-forward neural networks in NARX configuration","volume":"54","author":"Bonassi","year":"2021","journal-title":"IFAC-PapersOnLine"},{"issue":"5","key":"ref46","doi-asserted-by":"crossref","first-page":"487","DOI":"10.1002\/rnc.4590050508","article-title":"Discrete-time reference governors and the nonlinear control of systems with state and control constraints","volume":"5","author":"Gilbert","year":"1995","journal-title":"Int. J. Robust Nonlin. Control"},{"key":"ref47","doi-asserted-by":"crossref","DOI":"10.1016\/j.ejcon.2022.100632","article-title":"Recurrent neural network-based internal model control design for stable nonlinear systems","volume":"65","author":"Bonassi","year":"2022","journal-title":"Eur. J. Control"},{"key":"ref48","volume-title":"Robust Process Control","author":"Morari","year":"1989"},{"issue":"1","key":"ref49","doi-asserted-by":"crossref","first-page":"5698","DOI":"10.1038\/s41467-023-41379-3","article-title":"Model-free tracking control of complex dynamical trajectories with machine learning","volume":"14","author":"Zhai","year":"2023","journal-title":"Nature Commun."},{"issue":"10","key":"ref50","doi-asserted-by":"crossref","first-page":"2665","DOI":"10.1007\/s00500-015-1966-0","article-title":"An inverse controller design method for interval type-2 fuzzy models","volume":"21","author":"Kumbasar","year":"2017","journal-title":"Soft Comput."},{"key":"ref51","doi-asserted-by":"publisher","DOI":"10.1016\/0098-1354(95)00113-g"},{"key":"ref52","volume-title":"Deep Learning","author":"Goodfellow","year":"2016"},{"issue":"1","key":"ref53","doi-asserted-by":"crossref","first-page":"126","DOI":"10.1109\/59.651623","article-title":"Recurrent neural networks for short-term load forecasting","volume":"13","author":"Vermaak","year":"1998","journal-title":"IEEE Trans. Power Syst."},{"key":"ref54","doi-asserted-by":"publisher","DOI":"10.1016\/j.sysconle.2021.105049"}],"container-title":["IEEE Transactions on Automation Science and Engineering"],"original-title":[],"link":[{"URL":"http:\/\/xplorestaging.ieee.org\/ielx8\/8856\/10839176\/10729651.pdf?arnumber=10729651","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,4,4]],"date-time":"2025-04-04T14:23:32Z","timestamp":1743776612000},"score":1,"resource":{"primary":{"URL":"https:\/\/ieeexplore.ieee.org\/document\/10729651\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025]]},"references-count":54,"URL":"https:\/\/doi.org\/10.1109\/tase.2024.3479321","relation":{},"ISSN":["1545-5955","1558-3783"],"issn-type":[{"value":"1545-5955","type":"print"},{"value":"1558-3783","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025]]}}}