{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,18]],"date-time":"2026-01-18T06:11:28Z","timestamp":1768716688816,"version":"3.49.0"},"reference-count":37,"publisher":"Springer Science and Business Media LLC","issue":"20","license":[{"start":{"date-parts":[[2024,4,21]],"date-time":"2024-04-21T00:00:00Z","timestamp":1713657600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2024,4,21]],"date-time":"2024-04-21T00:00:00Z","timestamp":1713657600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"funder":[{"DOI":"10.13039\/501100012166","name":"National Key R&D Program of China","doi-asserted-by":"crossref","award":["Grant 2022YFB4700200 and Grant 2022YFB4700204"],"award-info":[{"award-number":["Grant 2022YFB4700200 and Grant 2022YFB4700204"]}],"id":[{"id":"10.13039\/501100012166","id-type":"DOI","asserted-by":"crossref"}]},{"name":"Knowledge Innovation Program of Wuhan - Basic Research","award":["Grant 2023010201010055"],"award-info":[{"award-number":["Grant 2023010201010055"]}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["Grant 62103157"],"award-info":[{"award-number":["Grant 62103157"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Neural Comput & Applic"],"published-print":{"date-parts":[[2024,7]]},"DOI":"10.1007\/s00521-024-09666-2","type":"journal-article","created":{"date-parts":[[2024,4,21]],"date-time":"2024-04-21T19:01:25Z","timestamp":1713726085000},"page":"12371-12383","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["Model predictive control for a bending pneumatic muscle based on an online modified generalized Prandtl\u2013Ishlinskii model"],"prefix":"10.1007","volume":"36","author":[{"given":"Hongge","family":"Ru","sequence":"first","affiliation":[]},{"given":"Yuqi","family":"Yang","sequence":"additional","affiliation":[]},{"given":"Bo","family":"Wang","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6267-8824","authenticated-orcid":false,"given":"Jian","family":"Huang","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2024,4,21]]},"reference":[{"key":"9666_CR1","unstructured":"Morin AH. Elastic diaphragm. U.S. Patent No. 2,642,091"},{"key":"9666_CR2","doi-asserted-by":"publisher","first-page":"63","DOI":"10.1016\/j.robot.2017.10.010","volume":"99","author":"H Al-Fahaam","year":"2018","unstructured":"Al-Fahaam H, Davis S, Nefti-Meziani S (2018) The design and mathematical modelling of novel extensor bending pneumatic artificial muscles (EBPAMs) for soft exoskeletons. Robot Auton Syst 99:63\u201374. https:\/\/doi.org\/10.1016\/j.robot.2017.10.010","journal-title":"Robot Auton Syst"},{"key":"9666_CR3","doi-asserted-by":"publisher","first-page":"502","DOI":"10.1109\/lra.2021.3123747","volume":"7","author":"Q Liu","year":"2022","unstructured":"Liu Q et al (2022) Design and hierarchical force-position control of redundant pneumatic muscles-cable-driven ankle rehabilitation robot. IEEE Robot Autom Lett 7:502\u2013509. https:\/\/doi.org\/10.1109\/lra.2021.3123747","journal-title":"IEEE Robot Autom Lett"},{"key":"9666_CR4","doi-asserted-by":"publisher","first-page":"2162","DOI":"10.1109\/tase.2020.2992890","volume":"17","author":"B Zhong","year":"2020","unstructured":"Zhong B, Cao J, McDaid A, Xie SQ, Zhang M (2020) Synchronous position and compliance regulation on a bi-joint gait exoskeleton driven by pneumatic muscles. IEEE Trans Autom Sci Eng 17:2162\u20132166. https:\/\/doi.org\/10.1109\/tase.2020.2992890","journal-title":"IEEE Trans Autom Sci Eng"},{"key":"9666_CR5","doi-asserted-by":"publisher","unstructured":"Arachchige DD, Chen Y, Walker ID, Godage IS (2021) A novel variable stiffness soft robotic gripper (IEEE 2021). https:\/\/doi.org\/10.1109\/case49439.2021.9551616","DOI":"10.1109\/case49439.2021.9551616"},{"key":"9666_CR6","doi-asserted-by":"publisher","first-page":"81","DOI":"10.1089\/soro.2016.0079","volume":"5","author":"J Yi","year":"2018","unstructured":"Yi J, Chen X, Song C, Wang Z (2018) Fiber-reinforced origamic robotic actuator. Soft Robot 5:81\u201392. https:\/\/doi.org\/10.1089\/soro.2016.0079","journal-title":"Soft Robot"},{"key":"9666_CR7","doi-asserted-by":"publisher","first-page":"5253","DOI":"10.1109\/lra.2021.3072813","volume":"6","author":"F Chen","year":"2021","unstructured":"Chen F, Miao Y, Gu G, Zhu X (2021) Soft twisting pneumatic actuators enabled by freeform surface design. IEEE Robot Autom Lett 6:5253\u20135260. https:\/\/doi.org\/10.1109\/lra.2021.3072813","journal-title":"IEEE Robot Autom Lett"},{"key":"9666_CR8","doi-asserted-by":"crossref","unstructured":"Liu X, Zhang J, Gu S, Zhao L, Li Z (2023) Modelling and angle tracking control for multi-chamber soft bending pneumatic muscle. IEEE Robot Autom Lett","DOI":"10.1109\/LRA.2023.3322072"},{"key":"9666_CR9","doi-asserted-by":"publisher","first-page":"550","DOI":"10.1089\/soro.2019.0065","volume":"7","author":"P Abbasi","year":"2020","unstructured":"Abbasi P, Nekoui MA, Zareinejad M, Abbasi P, Azhang Z (2020) Position and force control of a soft pneumatic actuator. Soft Rob 7:550\u2013563","journal-title":"Soft Rob"},{"key":"9666_CR10","doi-asserted-by":"publisher","DOI":"10.1016\/j.mechmachtheory.2022.105169","volume":"181","author":"H Ru","year":"2023","unstructured":"Ru H, Huang J, Chen W, Xiong C (2023) Modeling and identification of rate-dependent and asymmetric hysteresis of soft bending pneumatic actuator based on evolutionary firefly algorithm. Mech Mach Theory 181:105169. https:\/\/doi.org\/10.1016\/j.mechmachtheory.2022.105169","journal-title":"Mech Mach Theory"},{"key":"9666_CR11","doi-asserted-by":"publisher","first-page":"49","DOI":"10.1016\/j.mechatronics.2018.04.001","volume":"52","author":"S-L Xie","year":"2018","unstructured":"Xie S-L, Liu H-T, Mei J-P, Gu G-Y (2018) Modeling and compensation of asymmetric hysteresis for pneumatic artificial muscles with a modified generalized prandtl\u2013ishlinskii model. Mechatronics 52:49\u201357. https:\/\/doi.org\/10.1016\/j.mechatronics.2018.04.001","journal-title":"Mechatronics"},{"key":"9666_CR12","doi-asserted-by":"publisher","first-page":"122","DOI":"10.3390\/act11050122","volume":"11","author":"H Ji","year":"2022","unstructured":"Ji H et al (2022) Modeling and control of hysteresis characteristics of piezoelectric micro-positioning platform based on Duhem model. Actuators 11:122. https:\/\/doi.org\/10.3390\/act11050122","journal-title":"Actuators"},{"key":"9666_CR13","doi-asserted-by":"publisher","first-page":"491","DOI":"10.12693\/aphyspola.120.491","volume":"120","author":"N Pop","year":"2011","unstructured":"Pop N, Caltun O (2011) Jiles\u2013Atherton magnetic hysteresis parameters identification. Acta Phys Pol A 120:491\u2013496. https:\/\/doi.org\/10.12693\/aphyspola.120.491","journal-title":"Acta Phys Pol A"},{"key":"9666_CR14","doi-asserted-by":"publisher","first-page":"7502","DOI":"10.1109\/tnnls.2021.3085321","volume":"33","author":"G Chen","year":"2022","unstructured":"Chen G, Chen G, Lou Y (2022) Diagonal recurrent neural network-based hysteresis modeling. IEEE Trans Neural Netw Learn Syst 33:7502\u20137512. https:\/\/doi.org\/10.1109\/tnnls.2021.3085321","journal-title":"IEEE Trans Neural Netw Learn Syst"},{"key":"9666_CR15","doi-asserted-by":"publisher","first-page":"835","DOI":"10.1016\/j.ymssp.2017.09.004","volume":"104","author":"MA Janaideh","year":"2018","unstructured":"Janaideh MA, Aljanaideh O (2018) Further results on open-loop compensation of rate-dependent hysteresis in a magnetostrictive actuator with the prandtl-ishlinskii model. Mech Syst Signal Process 104:835\u2013850. https:\/\/doi.org\/10.1016\/j.ymssp.2017.09.004","journal-title":"Mech Syst Signal Process"},{"key":"9666_CR16","doi-asserted-by":"publisher","first-page":"30","DOI":"10.1109\/MCS.2023.3253419","volume":"43","author":"C Della Santina","year":"2023","unstructured":"Della Santina C, Duriez C, Rus D (2023) Model-based control of soft robots: a survey of the state of the art and open challenges. IEEE Control Syst Mag 43:30\u201365","journal-title":"IEEE Control Syst Mag"},{"key":"9666_CR17","doi-asserted-by":"publisher","DOI":"10.1016\/j.ymssp.2020.107532","volume":"154","author":"S Shakiba","year":"2021","unstructured":"Shakiba S, Ourak M, Poorten EV, Ayati M, Yousefi-Koma A (2021) Modeling and compensation of asymmetric rate-dependent hysteresis of a miniature pneumatic artificial muscle-based catheter. Mech Syst Signal Process 154:107532. https:\/\/doi.org\/10.1016\/j.ymssp.2020.107532","journal-title":"Mech Syst Signal Process"},{"key":"9666_CR18","doi-asserted-by":"publisher","first-page":"2023","DOI":"10.1007\/s11071-022-07324-7","volume":"108","author":"L Nie","year":"2022","unstructured":"Nie L, Luo Y, Gao W, Zhou M (2022) Rate-dependent asymmetric hysteresis modeling and robust adaptive trajectory tracking for piezoelectric micropositioning stages. Nonlinear Dyn 108:2023\u20132043. https:\/\/doi.org\/10.1007\/s11071-022-07324-7","journal-title":"Nonlinear Dyn"},{"key":"9666_CR19","doi-asserted-by":"publisher","first-page":"170","DOI":"10.1016\/j.automatica.2015.04.012","volume":"57","author":"J Zhang","year":"2015","unstructured":"Zhang J, Merced E, Sep\u00falveda N, Tan X (2015) Optimal compression of generalized Prandtl\u2013Ishlinskii hysteresis models. Automatica 57:170\u2013179. https:\/\/doi.org\/10.1016\/j.automatica.2015.04.012","journal-title":"Automatica"},{"key":"9666_CR20","doi-asserted-by":"publisher","first-page":"531","DOI":"10.1016\/j.ifacol.2015.09.022","volume":"48","author":"MG Forbes","year":"2015","unstructured":"Forbes MG, Patwardhan RS, Hamadah H, Gopaluni RB (2015) Model predictive control in industry: challenges and opportunities. IFAC-PapersOnLine 48:531\u2013538. https:\/\/doi.org\/10.1016\/j.ifacol.2015.09.022","journal-title":"IFAC-PapersOnLine"},{"key":"9666_CR21","doi-asserted-by":"publisher","first-page":"382","DOI":"10.1109\/tpel.2019.2915675","volume":"35","author":"X Hu","year":"2020","unstructured":"Hu X, Zou C, Tang X, Liu T, Hu L (2020) Cost-optimal energy management of hybrid electric vehicles using fuel cell\/battery health-aware predictive control. IEEE Trans Power Electron 35:382\u2013392. https:\/\/doi.org\/10.1109\/tpel.2019.2915675","journal-title":"IEEE Trans Power Electron"},{"key":"9666_CR22","doi-asserted-by":"publisher","first-page":"935","DOI":"10.1109\/tie.2016.2625238","volume":"64","author":"S Vazquez","year":"2017","unstructured":"Vazquez S, Rodriguez J, Rivera M, Franquelo LG, Norambuena M (2017) Model predictive control for power converters and drives: advances and trends. IEEE Trans Industr Electron 64:935\u2013947. https:\/\/doi.org\/10.1109\/tie.2016.2625238","journal-title":"IEEE Trans Industr Electron"},{"key":"9666_CR23","doi-asserted-by":"publisher","first-page":"505","DOI":"10.1109\/tie.2016.2606358","volume":"64","author":"H Xiao","year":"2017","unstructured":"Xiao H et al (2017) Robust stabilization of a wheeled mobile robot using model predictive control based on neurodynamics optimization. IEEE Trans Industr Electron 64:505\u2013516. https:\/\/doi.org\/10.1109\/tie.2016.2606358","journal-title":"IEEE Trans Industr Electron"},{"key":"9666_CR24","doi-asserted-by":"publisher","first-page":"3689","DOI":"10.1109\/tie.2021.3076721","volume":"69","author":"D Wang","year":"2022","unstructured":"Wang D et al (2022) Model predictive control using artificial neural network for power converters. IEEE Trans Industr Electron 69:3689\u20133699. https:\/\/doi.org\/10.1109\/tie.2021.3076721","journal-title":"IEEE Trans Industr Electron"},{"key":"9666_CR25","doi-asserted-by":"publisher","unstructured":"Chen, S, et\u00a0al (2018) Approximating explicit model predictive control using constrained neural networks (IEEE, 2018). https:\/\/doi.org\/10.23919\/acc.2018.8431275","DOI":"10.23919\/acc.2018.8431275"},{"key":"9666_CR26","doi-asserted-by":"publisher","first-page":"2967","DOI":"10.1016\/j.automatica.2014.10.128","volume":"50","author":"DQ Mayne","year":"2014","unstructured":"Mayne DQ (2014) Model predictive control: recent developments and future promise. Automatica 50:2967\u20132986. https:\/\/doi.org\/10.1016\/j.automatica.2014.10.128","journal-title":"Automatica"},{"key":"9666_CR27","doi-asserted-by":"publisher","unstructured":"Ru H, Huang J, Chen W, Xiong C, Wang J (2018) Design and control of a soft bending pneumatic actuator based on visual feedback (IEEE, 2018). https:\/\/doi.org\/10.1109\/wcica.2018.8630440","DOI":"10.1109\/wcica.2018.8630440"},{"key":"9666_CR28","doi-asserted-by":"publisher","first-page":"662","DOI":"10.1089\/soro.2017.0076","volume":"5","author":"L Cappello","year":"2018","unstructured":"Cappello L et al (2018) Exploiting textile mechanical anisotropy for fabric-based pneumatic actuators. Soft Rob 5:662\u2013674. https:\/\/doi.org\/10.1089\/soro.2017.0076","journal-title":"Soft Rob"},{"key":"9666_CR29","doi-asserted-by":"publisher","first-page":"778","DOI":"10.1109\/tro.2015.2428504","volume":"31","author":"P Polygerinos","year":"2015","unstructured":"Polygerinos P et al (2015) Modeling of soft fiber-reinforced bending actuators. IEEE Trans Rob 31:778\u2013789. https:\/\/doi.org\/10.1109\/tro.2015.2428504","journal-title":"IEEE Trans Rob"},{"key":"9666_CR30","doi-asserted-by":"publisher","first-page":"8455","DOI":"10.1109\/tie.2020.3013544","volume":"68","author":"M Luo","year":"2021","unstructured":"Luo M et al (2021) A single-chamber pneumatic soft bending actuator with increased stroke-range by local electric guidance. IEEE Trans Industr Electron 68:8455\u20138463. https:\/\/doi.org\/10.1109\/tie.2020.3013544","journal-title":"IEEE Trans Industr Electron"},{"key":"9666_CR31","doi-asserted-by":"publisher","first-page":"24","DOI":"10.1089\/soro.2016.0052","volume":"5","author":"G Alici","year":"2018","unstructured":"Alici G, Canty T, Mutlu R, Hu W, Sencadas V (2018) Modeling and experimental evaluation of bending behavior of soft pneumatic actuators made of discrete actuation chambers. Soft Rob 5:24\u201335. https:\/\/doi.org\/10.1089\/soro.2016.0052","journal-title":"Soft Rob"},{"key":"9666_CR32","doi-asserted-by":"publisher","first-page":"1376","DOI":"10.1002\/adfm.201102978","volume":"22","author":"RV Martinez","year":"2012","unstructured":"Martinez RV, Fish CR, Chen X, Whitesides GM (2012) Elastomeric origami: programmable paper-elastomer composites as pneumatic actuators. Adv Func Mater 22:1376\u20131384. https:\/\/doi.org\/10.1002\/adfm.201102978","journal-title":"Adv Func Mater"},{"key":"9666_CR33","doi-asserted-by":"publisher","first-page":"411","DOI":"10.1177\/0278364920979367","volume":"40","author":"H Jiang","year":"2021","unstructured":"Jiang H et al (2021) Hierarchical control of soft manipulators towards unstructured interactions. Int J Robot Res 40:411\u2013434. https:\/\/doi.org\/10.1177\/0278364920979367","journal-title":"Int J Robot Res"},{"key":"9666_CR34","doi-asserted-by":"publisher","unstructured":"Rakotondrabe M (2012) Classical Prandtl\u2013Ishlinskii modeling and inverse multiplicative structure to compensate hysteresis in piezoactuators (IEEE, 2012). https:\/\/doi.org\/10.1109\/acc.2012.6314620","DOI":"10.1109\/acc.2012.6314620"},{"key":"9666_CR35","doi-asserted-by":"publisher","first-page":"5962","DOI":"10.1109\/TIE.2021.3090708","volume":"69","author":"C Chen","year":"2021","unstructured":"Chen C, Huang J, Wu D, Tu X (2021) Interval type-2 fuzzy disturbance observer-based t-s fuzzy control for a pneumatic flexible joint. IEEE Trans Industr Electron 69:5962\u20135972","journal-title":"IEEE Trans Industr Electron"},{"key":"9666_CR36","doi-asserted-by":"publisher","first-page":"5107","DOI":"10.1109\/TMECH.2022.3172715","volume":"27","author":"M Zhang","year":"2022","unstructured":"Zhang M, Huang J, Cao Y, Xiong C-H, Mohammed S (2022) Echo state network-enhanced super-twisting control of passive gait training exoskeleton driven by pneumatic muscles. IEEE\/ASME Trans Mechatron 27:5107\u20135118","journal-title":"IEEE\/ASME Trans Mechatron"},{"key":"9666_CR37","doi-asserted-by":"publisher","first-page":"6281","DOI":"10.1016\/j.jfranklin.2021.06.020","volume":"358","author":"RB Anderson","year":"2021","unstructured":"Anderson RB, Marshall JA, L\u2019Afflitto A (2021) Novel model reference adaptive control laws for improved transient dynamics and guaranteed saturation constraints. J Franklin Inst 358:6281\u20136308","journal-title":"J Franklin Inst"}],"container-title":["Neural Computing and Applications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00521-024-09666-2.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s00521-024-09666-2\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00521-024-09666-2.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,7,8]],"date-time":"2024-07-08T14:15:21Z","timestamp":1720448121000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s00521-024-09666-2"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,4,21]]},"references-count":37,"journal-issue":{"issue":"20","published-print":{"date-parts":[[2024,7]]}},"alternative-id":["9666"],"URL":"https:\/\/doi.org\/10.1007\/s00521-024-09666-2","relation":{},"ISSN":["0941-0643","1433-3058"],"issn-type":[{"value":"0941-0643","type":"print"},{"value":"1433-3058","type":"electronic"}],"subject":[],"published":{"date-parts":[[2024,4,21]]},"assertion":[{"value":"25 September 2023","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"25 March 2024","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"21 April 2024","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 they have no conflicts of interest or personal relationships that could have appeared to influence the work reported in this paper.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}}]}}