{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,4]],"date-time":"2026-07-04T07:19:27Z","timestamp":1783149567062,"version":"3.54.6"},"reference-count":40,"publisher":"Elsevier BV","license":[{"start":{"date-parts":[[2026,10,1]],"date-time":"2026-10-01T00:00:00Z","timestamp":1790812800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/tdm\/userlicense\/1.0\/"},{"start":{"date-parts":[[2026,10,1]],"date-time":"2026-10-01T00:00:00Z","timestamp":1790812800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/legal\/tdmrep-license"},{"start":{"date-parts":[[2026,10,1]],"date-time":"2026-10-01T00:00:00Z","timestamp":1790812800000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-017"},{"start":{"date-parts":[[2026,10,1]],"date-time":"2026-10-01T00:00:00Z","timestamp":1790812800000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-037"},{"start":{"date-parts":[[2026,10,1]],"date-time":"2026-10-01T00:00:00Z","timestamp":1790812800000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-012"},{"start":{"date-parts":[[2026,10,1]],"date-time":"2026-10-01T00:00:00Z","timestamp":1790812800000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-029"},{"start":{"date-parts":[[2026,10,1]],"date-time":"2026-10-01T00:00:00Z","timestamp":1790812800000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-004"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["2025YZ39"],"award-info":[{"award-number":["2025YZ39"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100011311","name":"State Key Laboratory of Industrial Control Technology","doi-asserted-by":"publisher","award":["ICT2025D13"],"award-info":[{"award-number":["ICT2025D13"]}],"id":[{"id":"10.13039\/501100011311","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100011311","name":"State Key Laboratory of Industrial Control Technology","doi-asserted-by":"publisher","award":["ICT2025B71"],"award-info":[{"award-number":["ICT2025B71"]}],"id":[{"id":"10.13039\/501100011311","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["elsevier.com","sciencedirect.com"],"crossmark-restriction":true},"short-container-title":["Engineering Applications of Artificial Intelligence"],"published-print":{"date-parts":[[2026,10]]},"DOI":"10.1016\/j.engappai.2026.115315","type":"journal-article","created":{"date-parts":[[2026,6,11]],"date-time":"2026-06-11T13:33:23Z","timestamp":1781184803000},"page":"115315","update-policy":"https:\/\/doi.org\/10.1016\/elsevier_cm_policy","source":"Crossref","is-referenced-by-count":0,"special_numbering":"P1","title":["Lipschitz bounded deep Koopman for robust modeling and offset-free predictive control of disturbed Organic Rankine Cycle system"],"prefix":"10.1016","volume":"181","author":[{"given":"Zhanpeng","family":"Bao","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6557-6823","authenticated-orcid":false,"given":"Yao","family":"Shi","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yitian","family":"Wang","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Xialai","family":"Wu","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Entao","family":"Sun","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Hongye","family":"Su","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Lei","family":"Xie","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"78","reference":[{"key":"10.1016\/j.engappai.2026.115315_b1","doi-asserted-by":"crossref","DOI":"10.1016\/j.energy.2024.132829","article-title":"Integration and optimization of a waste heat driven organic rankine cycle for power generation in wastewater treatment plants","volume":"308","author":"Alrbai","year":"2024","journal-title":"Energy"},{"key":"10.1016\/j.engappai.2026.115315_b2","doi-asserted-by":"crossref","DOI":"10.1016\/j.mechatronics.2022.102871","article-title":"Offset-free model predictive control of a soft manipulator using the koopman operator","volume":"86","author":"Chen","year":"2022","journal-title":"Mechatronics"},{"key":"10.1016\/j.engappai.2026.115315_b3","doi-asserted-by":"crossref","DOI":"10.1016\/j.conengprac.2020.104519","article-title":"Superheating control of an organic rankine cycle for recovering waste heat from an engine cooling system","volume":"101","author":"Dubuc","year":"2020","journal-title":"Control Eng. Pract."},{"issue":"65","key":"10.1016\/j.engappai.2026.115315_b4","first-page":"1","article-title":"Improving Lipschitz-constrained neural networks by learning activation functions","volume":"25","author":"Ducotterd","year":"2024","journal-title":"J. Mach. Learn. Res."},{"key":"10.1016\/j.engappai.2026.115315_b5","unstructured":"Erichson, N.B., Azencot, O., Queiruga, A., Hodgkinson, L., Mahoney, M.W., 2021. Lipschitz Recurrent Neural Networks. In: 9th International Conference on Learning Representations, ICLR."},{"issue":"15","key":"10.1016\/j.engappai.2026.115315_b6","doi-asserted-by":"crossref","first-page":"411","DOI":"10.1016\/j.ifacol.2015.10.059","article-title":"Nonlinear model predictive control of an organic rankine cycle for exhaust waste heat recovery in automotive engines","volume":"48","author":"Esposito","year":"2015","journal-title":"IFAC-PapersOnLine"},{"key":"10.1016\/j.engappai.2026.115315_b7","doi-asserted-by":"crossref","DOI":"10.1016\/j.enconman.2022.115493","article-title":"Experimental characterization of a small-scale solar organic rankine cycle (ORC) based unit for domestic microcogeneration","volume":"258","author":"Fatigati","year":"2022","journal-title":"Energy Convers. Manage."},{"issue":"10","key":"10.1016\/j.engappai.2026.115315_b8","doi-asserted-by":"crossref","first-page":"1475","DOI":"10.3390\/e25101475","article-title":"Advanced exergy-based analysis of an organic rankine cycle (ORC) for waste heat recovery","volume":"25","author":"Fergani","year":"2023","journal-title":"Entropy"},{"key":"10.1016\/j.engappai.2026.115315_b9","doi-asserted-by":"crossref","DOI":"10.1016\/j.compchemeng.2022.108029","article-title":"A probabilistic deep learning approach for thermal and exergy forecasting in organic rankine cycles","volume":"168","author":"Flores-Tlacuahuac","year":"2022","journal-title":"Comput. Chem. Eng."},{"key":"10.1016\/j.engappai.2026.115315_b10","series-title":"On the effectiveness of interval bound propagation for training verifiably robust models","author":"Gowal","year":"2018"},{"issue":"5","key":"10.1016\/j.engappai.2026.115315_b11","doi-asserted-by":"crossref","first-page":"315","DOI":"10.1073\/pnas.17.5.315","article-title":"Hamiltonian systems and transformation in Hilbert space","volume":"17","author":"Koopman","year":"1931","journal-title":"Proc. Natl. Acad. Sci. the USA"},{"key":"10.1016\/j.engappai.2026.115315_b12","doi-asserted-by":"crossref","first-page":"149","DOI":"10.1016\/j.automatica.2018.03.046","article-title":"Linear predictors for nonlinear dynamical systems: Koopman operator meets model predictive control","volume":"93","author":"Korda","year":"2018","journal-title":"Automatica"},{"issue":"2","key":"10.1016\/j.engappai.2026.115315_b13","doi-asserted-by":"crossref","first-page":"765","DOI":"10.3390\/en16020765","article-title":"Dynamic performance of organic rankine cycle driven by fluctuant industrial waste heat for building power supply","volume":"16","author":"Li","year":"2023","journal-title":"Energies"},{"key":"10.1016\/j.engappai.2026.115315_b14","doi-asserted-by":"crossref","first-page":"184","DOI":"10.1016\/j.egypro.2017.09.109","article-title":"Model predictive control of an organic rankine cycle system","volume":"129","author":"Liu","year":"2017","journal-title":"Energy Procedia"},{"issue":"10","key":"10.1016\/j.engappai.2026.115315_b15","doi-asserted-by":"crossref","first-page":"2214","DOI":"10.1016\/j.automatica.2009.06.005","article-title":"Linear offset-free model predictive control","volume":"45","author":"Maeder","year":"2009","journal-title":"Automatica"},{"issue":"4","key":"10.1016\/j.engappai.2026.115315_b16","article-title":"Machine learning for design and optimization of organic rankine cycle plants: A review of current status and future perspectives","volume":"12","author":"Oyekale","year":"2023","journal-title":"Wiley Interdiscip. Rev.: Energy Environ."},{"key":"10.1016\/j.engappai.2026.115315_b17","doi-asserted-by":"crossref","first-page":"72","DOI":"10.1016\/j.energy.2018.10.059","article-title":"Machine learning for the prediction of the dynamic behavior of a small scale ORC system","volume":"166","author":"Palagi","year":"2019","journal-title":"Energy"},{"key":"10.1016\/j.engappai.2026.115315_b18","doi-asserted-by":"crossref","DOI":"10.3389\/fenrg.2024.1474714","article-title":"Thermodynamic analysis of a cascade organic rankine cycle power generation system driven by hybrid geothermal energy and liquefied natural gas","volume":"12","author":"Pan","year":"2024","journal-title":"Front. Energy Res."},{"key":"10.1016\/j.engappai.2026.115315_b19","series-title":"2015 European Control Conference","first-page":"527","article-title":"Offset-free tracking MPC: A tutorial review and comparison of different formulations","author":"Pannocchia","year":"2015"},{"issue":"23","key":"10.1016\/j.engappai.2026.115315_b20","doi-asserted-by":"crossref","first-page":"342","DOI":"10.1016\/j.ifacol.2015.11.304","article-title":"Offset-free MPC explained: novelties, subtleties, and applications","volume":"48","author":"Pannocchia","year":"2015","journal-title":"IFAC-PapersOnLine"},{"key":"10.1016\/j.engappai.2026.115315_b21","series-title":"2012 IEEE Vehicle Power and Propulsion Conference","first-page":"289","article-title":"Towards model-based control of a steam rankine process for engine waste heat recovery","author":"Peralez","year":"2012"},{"key":"10.1016\/j.engappai.2026.115315_b22","doi-asserted-by":"crossref","DOI":"10.1016\/j.engappai.2023.106979","article-title":"Ensemble learning-based nonlinear time series prediction and dynamic multi-objective optimization of organic rankine cycle (ORC) under actual driving cycle","volume":"126","author":"Ping","year":"2023","journal-title":"Eng. Appl. Artif. Intell."},{"key":"10.1016\/j.engappai.2026.115315_b23","doi-asserted-by":"crossref","DOI":"10.1016\/j.energy.2022.123438","article-title":"Energy, economic and environmental dynamic response characteristics of organic rankine cycle (ORC) system under different driving cycles","volume":"246","author":"Ping","year":"2022","journal-title":"Energy"},{"key":"10.1016\/j.engappai.2026.115315_b24","doi-asserted-by":"crossref","DOI":"10.1016\/j.engappai.2023.106744","article-title":"An efficient multilayer adaptive self-organizing modeling methodology for improving the generalization ability of organic rankine cycle (ORC) data-driven model","volume":"126","author":"Ping","year":"2023","journal-title":"Eng. Appl. Artif. Intell."},{"key":"10.1016\/j.engappai.2026.115315_b25","doi-asserted-by":"crossref","DOI":"10.1016\/j.applthermaleng.2023.121256","article-title":"An integrated online dynamic modeling scheme for organic rankine cycle (ORC): Adaptive self-organizing mechanism and convergence evaluation","volume":"234","author":"Ping","year":"2023","journal-title":"Appl. Therm. Eng."},{"issue":"2","key":"10.1016\/j.engappai.2026.115315_b26","doi-asserted-by":"crossref","first-page":"275","DOI":"10.1007\/s10514-018-9791-9","article-title":"Learning control Lyapunov functions from counterexamples and demonstrations","volume":"43","author":"Ravanbakhsh","year":"2019","journal-title":"Auton. Robots"},{"key":"10.1016\/j.engappai.2026.115315_b27","doi-asserted-by":"crossref","DOI":"10.1016\/j.conengprac.2023.105679","article-title":"Data-driven identification and fast model predictive control of the orc waste heat recovery system by using koopman operator","volume":"141","author":"Shi","year":"2023","journal-title":"Control Eng. Pract."},{"key":"10.1016\/j.engappai.2026.115315_b28","doi-asserted-by":"crossref","DOI":"10.1016\/j.energy.2021.122664","article-title":"Dual-mode fast DMC algorithm for the control of ORC based waste heat recovery system","volume":"244","author":"Shi","year":"2022","journal-title":"Energy"},{"key":"10.1016\/j.engappai.2026.115315_b29","doi-asserted-by":"crossref","DOI":"10.1016\/j.energy.2023.126959","article-title":"Data-driven model identification and efficient MPC via quasi-linear parameter varying representation for ORC waste heat recovery system","volume":"271","author":"Shi","year":"2023","journal-title":"Energy"},{"issue":"1","key":"10.1016\/j.engappai.2026.115315_b30","doi-asserted-by":"crossref","first-page":"94","DOI":"10.1002\/ese3.1962","article-title":"Enhanced modeling and control of organic rankine cycle systems via AM-LSTM networks based nonlinear MPC","volume":"13","author":"Sun","year":"2025","journal-title":"Energy Sci. Eng."},{"key":"10.1016\/j.engappai.2026.115315_b31","doi-asserted-by":"crossref","DOI":"10.1016\/j.engappai.2024.109946","article-title":"Intelligent modeling and analysis of hybrid organic rankine plants: Data-driven insights into thermodynamic efficiency and economic viability","volume":"143","author":"Tao","year":"2025","journal-title":"Eng. Appl. Artif. Intell."},{"key":"10.1016\/j.engappai.2026.115315_b32","doi-asserted-by":"crossref","DOI":"10.1016\/j.energy.2022.124027","article-title":"Performance prediction of a cryogenic organic rankine cycle based on back propagation neural network optimized by genetic algorithm","volume":"254","author":"Tian","year":"2022","journal-title":"Energy"},{"key":"10.1016\/j.engappai.2026.115315_b33","doi-asserted-by":"crossref","DOI":"10.1016\/j.enconman.2020.112700","article-title":"Application of machine learning into organic rankine cycle for prediction and optimization of thermal and exergy efficiency","volume":"210","author":"Wang","year":"2020","journal-title":"Energy Convers. Manage."},{"issue":"3","key":"10.1016\/j.engappai.2026.115315_b34","doi-asserted-by":"crossref","first-page":"3630","DOI":"10.1109\/TNNLS.2022.3194958","article-title":"Koopman-based MPC with learned dynamics: Hierarchical neural network approach","volume":"35","author":"Wang","year":"2022","journal-title":"IEEE Trans. Neural Networks Learn. Syst."},{"issue":"6","key":"10.1016\/j.engappai.2026.115315_b35","doi-asserted-by":"crossref","first-page":"1307","DOI":"10.1007\/s00332-015-9258-5","article-title":"A data\u2013driven approximation of the koopman operator: Extending dynamic mode decomposition","volume":"25","author":"Williams","year":"2015","journal-title":"J. Nonlinear Sci."},{"key":"10.1016\/j.engappai.2026.115315_b36","doi-asserted-by":"crossref","DOI":"10.1016\/j.applthermaleng.2024.124352","article-title":"Efficient predictive control method for ORC waste heat recovery system based on recurrent neural network","volume":"257","author":"Wu","year":"2024","journal-title":"Appl. Therm. Eng."},{"key":"10.1016\/j.engappai.2026.115315_b37","doi-asserted-by":"crossref","first-page":"251","DOI":"10.1016\/j.cjche.2024.09.004","article-title":"A fuzzy compensation-koopman model predictive control design for pressure regulation in proten exchange membrane electrolyzer","volume":"76","author":"Xiong","year":"2024","journal-title":"Chin. J. Chem. Eng."},{"key":"10.1016\/j.engappai.2026.115315_b38","doi-asserted-by":"crossref","first-page":"145","DOI":"10.1016\/j.rser.2019.03.012","article-title":"A comprehensive review of organic rankine cycle waste heat recovery systems in heavy-duty diesel engine applications","volume":"107","author":"Xu","year":"2019","journal-title":"Renew. Sustain. Energy Rev."},{"key":"10.1016\/j.engappai.2026.115315_b39","doi-asserted-by":"crossref","first-page":"15","DOI":"10.1016\/j.enconman.2018.02.062","article-title":"Artificial neural network (ANN) based prediction and optimization of an organic rankine cycle (ORC) for diesel engine waste heat recovery","volume":"164","author":"Yang","year":"2018","journal-title":"Energy Convers. Manage."},{"key":"10.1016\/j.engappai.2026.115315_b40","doi-asserted-by":"crossref","DOI":"10.1016\/j.egyai.2025.100519","article-title":"Bayesian optimized LSTM-based sensor fault diagnosis of organic rankine cycle system","author":"Zuo","year":"2025","journal-title":"Energy AI"}],"container-title":["Engineering Applications of Artificial Intelligence"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S095219762601599X?httpAccept=text\/xml","content-type":"text\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S095219762601599X?httpAccept=text\/plain","content-type":"text\/plain","content-version":"vor","intended-application":"text-mining"}],"deposited":{"date-parts":[[2026,7,4]],"date-time":"2026-07-04T06:51:39Z","timestamp":1783147899000},"score":1,"resource":{"primary":{"URL":"https:\/\/linkinghub.elsevier.com\/retrieve\/pii\/S095219762601599X"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,10]]},"references-count":40,"alternative-id":["S095219762601599X"],"URL":"https:\/\/doi.org\/10.1016\/j.engappai.2026.115315","relation":{},"ISSN":["0952-1976"],"issn-type":[{"value":"0952-1976","type":"print"}],"subject":[],"published":{"date-parts":[[2026,10]]},"assertion":[{"value":"Elsevier","name":"publisher","label":"This article is maintained by"},{"value":"Lipschitz bounded deep Koopman for robust modeling and offset-free predictive control of disturbed Organic Rankine Cycle system","name":"articletitle","label":"Article Title"},{"value":"Engineering Applications of Artificial Intelligence","name":"journaltitle","label":"Journal Title"},{"value":"https:\/\/doi.org\/10.1016\/j.engappai.2026.115315","name":"articlelink","label":"CrossRef DOI link to publisher maintained version"},{"value":"article","name":"content_type","label":"Content Type"},{"value":"\u00a9 2026 Published by Elsevier Ltd.","name":"copyright","label":"Copyright"}],"article-number":"115315"}}