{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,14]],"date-time":"2026-02-14T07:38:13Z","timestamp":1771054693437,"version":"3.50.1"},"reference-count":33,"publisher":"Springer Science and Business Media LLC","issue":"18","license":[{"start":{"date-parts":[[2025,3,29]],"date-time":"2025-03-29T00:00:00Z","timestamp":1743206400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2025,3,29]],"date-time":"2025-03-29T00:00:00Z","timestamp":1743206400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Neural Comput & Applic"],"published-print":{"date-parts":[[2025,6]]},"DOI":"10.1007\/s00521-025-11063-2","type":"journal-article","created":{"date-parts":[[2025,3,31]],"date-time":"2025-03-31T22:34:59Z","timestamp":1743460499000},"page":"12305-12328","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Embedded DNN-based nonlinear MPC with guaranteed constraint satisfaction"],"prefix":"10.1007","volume":"37","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-5537-6505","authenticated-orcid":false,"given":"Nirlipta Ranjan","family":"Mohanty","sequence":"first","affiliation":[]},{"given":"Promod","family":"Ubare","sequence":"additional","affiliation":[]},{"given":"Vaishali","family":"Patne","sequence":"additional","affiliation":[]},{"given":"Deepak","family":"Ingole","sequence":"additional","affiliation":[]},{"given":"Dayaram","family":"Sonawane","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2025,3,29]]},"reference":[{"key":"11063_CR1","doi-asserted-by":"crossref","unstructured":"Simonetti F, D\u2019Innocenzo A, Cecati C (2023) Neural network model predictive control for chb converters with fpga implementation. IEEE Trans Indus Inf","DOI":"10.1109\/TII.2023.3233973"},{"key":"11063_CR2","doi-asserted-by":"publisher","DOI":"10.1016\/j.apenergy.2022.119153","volume":"318","author":"M Elnour","year":"2022","unstructured":"Elnour M, Himeur Y, Fadli F, Mohammedsherif H, Meskin N, Ahmad AM, Petri I, Rezgui Y, Hodorog A (2022) Neural network-based model predictive control system for optimizing building automation and management systems of sports facilities. Appl Energy 318:119153","journal-title":"Appl Energy"},{"issue":"1","key":"11063_CR3","doi-asserted-by":"publisher","first-page":"409","DOI":"10.1109\/TII.2020.2969729","volume":"17","author":"S Lucia","year":"2020","unstructured":"Lucia S, Navarro D, Karg B, Sarnago H, Lucia O (2020) Deep learning-based model predictive control for resonant power converters. IEEE Trans Industr Inf 17(1):409\u2013420","journal-title":"IEEE Trans Industr Inf"},{"key":"11063_CR4","doi-asserted-by":"crossref","unstructured":"Mohanty NR, Jugade C, Patne V, Ingole D, Sonawane D (2022) Fpga implementation of low complexity nonlinear model predictive control using deep learning approach. In: 2022 Eighth Indian Control Conference (ICC), pp. 325\u2013330. IEEE","DOI":"10.1109\/ICC56513.2022.10093340"},{"key":"11063_CR5","doi-asserted-by":"crossref","unstructured":"Wang R, Li H, Liang B, Shi Y, Xu D (2023) Policy learning for nonlinear model predictive control with application to usvs. IEEE Transactions on Industrial Electronics","DOI":"10.1109\/TIE.2023.3274869"},{"key":"11063_CR6","doi-asserted-by":"crossref","unstructured":"Aouaichia A, Kara K, Benrabah M, Hadjili ML (2023) Constrained neural network model predictive controller based on archimedes optimization algorithm with application to robot manipulators. Journal of Control, Automation and Electrical Systems, 1\u201320","DOI":"10.1007\/s40313-023-01033-1"},{"key":"11063_CR7","doi-asserted-by":"crossref","unstructured":"Karg B, Lucia S (2020) Stability and feasibility of neural network-based controllers via output range analysis. In: 2020 59th IEEE Conference on Decision and Control (CDC), pp. 4947\u20134954. IEEE","DOI":"10.1109\/CDC42340.2020.9303895"},{"issue":"3","key":"11063_CR8","doi-asserted-by":"publisher","first-page":"719","DOI":"10.1109\/LCSYS.2020.2980479","volume":"4","author":"JA Paulson","year":"2020","unstructured":"Paulson JA, Mesbah A (2020) Approximate closed-loop robust model predictive control with guaranteed stability and constraint satisfaction. IEEE Control Syst Lett 4(3):719\u2013724","journal-title":"IEEE Control Syst Lett"},{"issue":"5","key":"11063_CR9","doi-asserted-by":"publisher","first-page":"2102","DOI":"10.1109\/TCST.2020.3024571","volume":"29","author":"X Zhang","year":"2020","unstructured":"Zhang X, Bujarbaruah M, Borrelli F (2020) Near-optimal rapid mpc using neural networks: a primal-dual policy learning framework. IEEE Trans Control Syst Technol 29(5):2102\u20132114","journal-title":"IEEE Trans Control Syst Technol"},{"key":"11063_CR10","unstructured":"Asadi F (2021) Constrained deep learning based nonlinear model predictive control. arXiv preprint arXiv:2103.13514"},{"key":"11063_CR11","unstructured":"Drgona J, Kis K, Tuor A, Vrabie D, Klauco M (2020) Differentiable predictive control: An mpc alternative for unknown nonlinear systems using constrained deep learning. arXiv preprint arXiv:2011.036991"},{"key":"11063_CR12","unstructured":"M\u00e1rquez-Neila P, Salzmann M, Fua P (2017) Imposing hard constraints on deep networks: Promises and limitations. arXiv preprint arXiv:1706.02025"},{"issue":"8","key":"11063_CR13","doi-asserted-by":"publisher","first-page":"2942","DOI":"10.1109\/TNNLS.2019.2934403","volume":"31","author":"Y-H Liu","year":"2019","unstructured":"Liu Y-H, Su C-Y, Li H, Lu R (2019) Barrier function-based adaptive control for uncertain strict-feedback systems within predefined neural network approximation sets. IEEE Trans Neural Netw Learn Syst 31(8):2942\u20132954","journal-title":"IEEE Trans Neural Netw Learn Syst"},{"key":"11063_CR14","doi-asserted-by":"crossref","unstructured":"Zhao Z, Zhang J, Liu Z, Mu C, Hong K-S (2022) Adaptive neural network control of an uncertain 2-dof helicopter with unknown backlash-like hysteresis and output constraints. IEEE Transactions on Neural Networks and Learning Systems","DOI":"10.1109\/TNNLS.2022.3163572"},{"key":"11063_CR15","doi-asserted-by":"publisher","first-page":"73474","DOI":"10.1109\/ACCESS.2022.3189353","volume":"10","author":"MC Maya-Rodriguez","year":"2022","unstructured":"Maya-Rodriguez MC, L\u00f3pez-Pacheco MA, Lozano-Hern\u00e1ndez Y, S\u00e1nchez-Meza VG, Cantera-Cantera LA, Tolentino-Eslava R (2022) Integration of cnn in a dynamic model-based controller for control of a 2dof helicopter with tail rotor perturbations. IEEE Access 10:73474\u201373483","journal-title":"IEEE Access"},{"issue":"3","key":"11063_CR16","doi-asserted-by":"publisher","first-page":"807","DOI":"10.1109\/JAS.2019.1911495","volume":"6","author":"Y Ouyang","year":"2019","unstructured":"Ouyang Y, Dong L, Xue L, Sun C (2019) Adaptive control based on neural networks for an uncertain 2-dof helicopter system with input deadzone and output constraints. IEEE\/CAA J Autom Sin 6(3):807\u2013815","journal-title":"IEEE\/CAA J Autom Sin"},{"issue":"5","key":"11063_CR17","doi-asserted-by":"publisher","first-page":"3967","DOI":"10.1109\/TIE.2019.2921296","volume":"67","author":"X Yang","year":"2019","unstructured":"Yang X, Zheng X (2019) Adaptive nn backstepping control design for a 3-dof helicopter: theory and experiments. IEEE Trans Industr Electron 67(5):3967\u20133979","journal-title":"IEEE Trans Industr Electron"},{"issue":"1","key":"11063_CR18","doi-asserted-by":"publisher","first-page":"182","DOI":"10.1080\/00207179.2021.1984583","volume":"96","author":"Y Wang","year":"2023","unstructured":"Wang Y, Yang J, Yang X, Wang T (2023) Adaptive neural network-based fault-tolerant control for a three degrees of freedom helicopter. Int J Control 96(1):182\u2013190","journal-title":"Int J Control"},{"key":"11063_CR19","doi-asserted-by":"publisher","DOI":"10.1201\/9781315272610","volume-title":"Model-based predictive control: a practical approach","author":"JA Rossiter","year":"2017","unstructured":"Rossiter JA (2017) Model-based predictive control: a practical approach. CRC Press, Boca Raton, FL"},{"issue":"2","key":"11063_CR20","doi-asserted-by":"publisher","first-page":"94","DOI":"10.1109\/MCS.2017.2786448","volume":"38","author":"EC Kerrigan","year":"2018","unstructured":"Kerrigan EC (2018) Predictive control for linear and hybrid systems [bookshelf]. IEEE Control Syst Mag 38(2):94\u201396","journal-title":"IEEE Control Syst Mag"},{"issue":"20","key":"11063_CR21","doi-asserted-by":"publisher","first-page":"511","DOI":"10.1016\/j.ifacol.2018.11.038","volume":"51","author":"S Lucia","year":"2018","unstructured":"Lucia S, Karg B (2018) A deep learning-based approach to robust nonlinear model predictive control. IFAC-PapersOnLine 51(20):511\u2013516","journal-title":"IFAC-PapersOnLine"},{"issue":"9","key":"11063_CR22","doi-asserted-by":"publisher","first-page":"3866","DOI":"10.1109\/TCYB.2020.2999556","volume":"50","author":"B Karg","year":"2020","unstructured":"Karg B, Lucia S (2020) Efficient representation and approximation of model predictive control laws via deep learning. IEEE Trans Cybernet 50(9):3866\u20133878","journal-title":"IEEE Trans Cybernet"},{"key":"11063_CR23","doi-asserted-by":"crossref","unstructured":"Heaton J (2018) Ian goodfellow, yoshua bengio, and aaron courville: Deep learning: The mit press, 2016, 800 pp, isbn: 0262035618. Genetic programming and evolvable machines 19(1-2), 305\u2013307","DOI":"10.1007\/s10710-017-9314-z"},{"key":"11063_CR24","doi-asserted-by":"crossref","unstructured":"Adhau S, Naik VV, Skogestad S (2021) Constrained neural networks for approximate nonlinear model predictive control. In: 2021 60th IEEE Conference on Decision and Control (CDC), pp. 295\u2013300. IEEE","DOI":"10.1109\/CDC45484.2021.9683320"},{"key":"11063_CR25","unstructured":"Freund RM (2004) Penalty and barrier methods for constrained optimization. Lecture Notes, Massachusetts Institute of Technology"},{"issue":"10","key":"11063_CR26","doi-asserted-by":"publisher","first-page":"12486","DOI":"10.1109\/TPEL.2022.3172681","volume":"37","author":"M Abu-Ali","year":"2022","unstructured":"Abu-Ali M, Berkel F, Manderla M, Reimann S, Kennel R, Abdelrahem M (2022) Deep learning-based long-horizon mpc: Robust, high performing, and computationally efficient control for pmsm drives. IEEE Trans Power Electron 37(10):12486\u201312501","journal-title":"IEEE Trans Power Electron"},{"key":"11063_CR27","doi-asserted-by":"crossref","unstructured":"Mohanty NR, Adhau S, Ingole D, Sonawane D (2021) Hardware implementation of low-complexity deep learning-based model predictive controller. In: 2021 European Control Conference (ECC), pp. 1024\u20131029. IEEE","DOI":"10.23919\/ECC54610.2021.9655061"},{"key":"11063_CR28","doi-asserted-by":"publisher","first-page":"165","DOI":"10.1016\/j.isatra.2018.01.027","volume":"74","author":"S Sadala","year":"2018","unstructured":"Sadala S, Patre B (2018) A new continuous sliding mode control approach with actuator saturation for control of 2-dof helicopter system. ISA Trans 74:165\u2013174","journal-title":"ISA Trans"},{"issue":"2","key":"11063_CR29","doi-asserted-by":"publisher","first-page":"7020","DOI":"10.1016\/j.ifacol.2020.12.443","volume":"53","author":"V Patne","year":"2020","unstructured":"Patne V, Ingole D, Sonawane D (2020) Fpga implementation framework for low latency nonlinear model predictive control. IFAC-PapersOnLine 53(2):7020\u20137025","journal-title":"IFAC-PapersOnLine"},{"key":"11063_CR30","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/s12532-018-0139-4","volume":"11","author":"JA Andersson","year":"2019","unstructured":"Andersson JA, Gillis J, Horn G, Rawlings JB, Diehl M (2019) Casadi: a software framework for nonlinear optimization and optimal control. Math Program Comput 11:1\u201336","journal-title":"Math Program Comput"},{"key":"11063_CR31","doi-asserted-by":"publisher","first-page":"25","DOI":"10.1007\/s10107-004-0559-y","volume":"106","author":"A W\u00e4chter","year":"2006","unstructured":"W\u00e4chter A, Biegler LT (2006) On the implementation of an interior-point filter line-search algorithm for large-scale nonlinear programming. Math Program 106:25\u201357","journal-title":"Math Program"},{"key":"11063_CR32","unstructured":"Adam KDBJ, et al (2014) A method for stochastic optimization. arXiv preprint arXiv:1412.69801412"},{"issue":"11","key":"11063_CR33","doi-asserted-by":"publisher","first-page":"16734","DOI":"10.1002\/aic.16734","volume":"65","author":"Z Wu","year":"2019","unstructured":"Wu Z, Tran A, Rincon D, Christofides PD (2019) Machine-learning-based predictive control of nonlinear processes. Part ii: computational implementation. AIChE J. 65(11):16734","journal-title":"AIChE J."}],"container-title":["Neural Computing and Applications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00521-025-11063-2.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s00521-025-11063-2\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00521-025-11063-2.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,6,17]],"date-time":"2025-06-17T14:54:49Z","timestamp":1750172089000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s00521-025-11063-2"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,3,29]]},"references-count":33,"journal-issue":{"issue":"18","published-print":{"date-parts":[[2025,6]]}},"alternative-id":["11063"],"URL":"https:\/\/doi.org\/10.1007\/s00521-025-11063-2","relation":{},"ISSN":["0941-0643","1433-3058"],"issn-type":[{"value":"0941-0643","type":"print"},{"value":"1433-3058","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,3,29]]},"assertion":[{"value":"22 December 2023","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"3 February 2025","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"29 March 2025","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"The authors declare that there is no Conflict of interest.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}}]}}