{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,27]],"date-time":"2026-08-27T17:17:31Z","timestamp":1787851051831,"version":"build-2784847793"},"reference-count":47,"publisher":"Elsevier BV","license":[{"start":{"date-parts":[[2026,9,1]],"date-time":"2026-09-01T00:00:00Z","timestamp":1788220800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/tdm\/userlicense\/1.0\/"},{"start":{"date-parts":[[2026,9,1]],"date-time":"2026-09-01T00:00:00Z","timestamp":1788220800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/legal\/tdmrep-license"},{"start":{"date-parts":[[2026,9,1]],"date-time":"2026-09-01T00:00:00Z","timestamp":1788220800000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-017"},{"start":{"date-parts":[[2026,9,1]],"date-time":"2026-09-01T00:00:00Z","timestamp":1788220800000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-037"},{"start":{"date-parts":[[2026,9,1]],"date-time":"2026-09-01T00:00:00Z","timestamp":1788220800000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-012"},{"start":{"date-parts":[[2026,9,1]],"date-time":"2026-09-01T00:00:00Z","timestamp":1788220800000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-029"},{"start":{"date-parts":[[2026,9,1]],"date-time":"2026-09-01T00:00:00Z","timestamp":1788220800000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-004"}],"funder":[{"DOI":"10.13039\/501100004000","name":"Guangzhou Municipal Science and Technology Program key projects","doi-asserted-by":"publisher","award":["2025A04J3036"],"award-info":[{"award-number":["2025A04J3036"]}],"id":[{"id":"10.13039\/501100004000","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100012226","name":"Fundamental Research Funds for the Central Universities","doi-asserted-by":"publisher","award":["21624201"],"award-info":[{"award-number":["21624201"]}],"id":[{"id":"10.13039\/501100012226","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["62206109"],"award-info":[{"award-number":["62206109"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["62472197"],"award-info":[{"award-number":["62472197"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["elsevier.com","sciencedirect.com"],"crossmark-restriction":true},"short-container-title":["Neurocomputing"],"published-print":{"date-parts":[[2026,9]]},"DOI":"10.1016\/j.neucom.2026.133923","type":"journal-article","created":{"date-parts":[[2026,5,12]],"date-time":"2026-05-12T02:25:56Z","timestamp":1778552756000},"page":"133923","update-policy":"https:\/\/doi.org\/10.1016\/elsevier_cm_policy","source":"Crossref","is-referenced-by-count":0,"special_numbering":"C","title":["RNN-based optimal consensus of high-order heterogeneous nonlinear MAS with input constraints"],"prefix":"10.1016","volume":"694","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-0463-0291","authenticated-orcid":false,"given":"Yinyan","family":"Zhang","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yuxuan","family":"Xiong","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jilian","family":"Zhang","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Guanggang","family":"Geng","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Shuai","family":"Li","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"78","reference":[{"issue":"8","key":"10.1016\/j.neucom.2026.133923_bib0005","doi-asserted-by":"crossref","first-page":"8188","DOI":"10.1109\/TITS.2023.3264608","article-title":"Consensus-based distributed cooperative perception for connected and automated vehicles","volume":"24","author":"Cai","year":"2023","journal-title":"IEEE Trans. Intell. Transp. Syst."},{"key":"10.1016\/j.neucom.2026.133923_bib0010","doi-asserted-by":"crossref","DOI":"10.1016\/j.ins.2025.122438","article-title":"Neural network-based collision-free optimal formation control for unmanned surface vehicles with the gain iterative disturbance observer","volume":"719","author":"Li","year":"2025","journal-title":"Inf. Sci."},{"issue":"9","key":"10.1016\/j.neucom.2026.133923_bib0015","doi-asserted-by":"crossref","first-page":"1520","DOI":"10.1109\/TAC.2004.834113","article-title":"Consensus problems in networks of agents with switching topology and time-delays","volume":"49","author":"Olfati-Saber","year":"2004","journal-title":"IEEE Trans. Autom. Control"},{"issue":"3","key":"10.1016\/j.neucom.2026.133923_bib0020","doi-asserted-by":"crossref","DOI":"10.1016\/j.jfranklin.2026.108403","article-title":"Distributed aggregative optimization for nonlinear multi-agent systems with state delays under time-varying graphs using sampling technology","volume":"363","author":"Li","year":"2025","journal-title":"J. Franklin Inst."},{"issue":"10","key":"10.1016\/j.neucom.2026.133923_bib0025","doi-asserted-by":"crossref","first-page":"6218","DOI":"10.1109\/TSMC.2019.2959394","article-title":"Optimal consensus via distributed protocol for second-order multiagent systems","volume":"51","author":"Sun","year":"2021","journal-title":"IEEE Trans. Syst. Man, Cybern. Syst."},{"issue":"7","key":"10.1016\/j.neucom.2026.133923_bib0030","doi-asserted-by":"crossref","first-page":"1315","DOI":"10.1109\/TCYB.2014.2350511","article-title":"Distributed cooperative optimal control for multiagent systems on directed graphs: an inverse optimal approach","volume":"45","author":"Zhang","year":"2015","journal-title":"IEEE Trans. Cybern."},{"issue":"8","key":"10.1016\/j.neucom.2026.133923_bib0035","doi-asserted-by":"crossref","first-page":"5320","DOI":"10.1109\/TSMC.2021.3120432","article-title":"Inverse-optimal consensus control of fractional-order multiagent systems","volume":"52","author":"An","year":"2022","journal-title":"IEEE Trans. Syst. Man, Cybern. Syst."},{"key":"10.1016\/j.neucom.2026.133923_bib0040","doi-asserted-by":"crossref","first-page":"10","DOI":"10.1016\/j.automatica.2018.01.024","article-title":"Receding horizon consensus of general linear multi-agent systems with input constraints: an inverse optimality approach","volume":"91","author":"Li","year":"2018","journal-title":"Automatica"},{"issue":"1","key":"10.1016\/j.neucom.2026.133923_bib0045","first-page":"102","article-title":"Distributed optimal consensus control algorithm for continuous-time multi-agent systems","volume":"67","author":"Wang","year":"2020","journal-title":"IEEE Trans. Circuits Syst. II Exp. Briefs"},{"issue":"8","key":"10.1016\/j.neucom.2026.133923_bib0050","doi-asserted-by":"crossref","first-page":"3339","DOI":"10.1109\/TNNLS.2017.2728622","article-title":"Distributed optimal consensus control for nonlinear multiagent system with unknown dynamic","volume":"29","author":"Zhang","year":"2018","journal-title":"IEEE Trans. Neural Netw. Learn. Syst."},{"issue":"4","key":"10.1016\/j.neucom.2026.133923_bib0055","doi-asserted-by":"crossref","first-page":"1482","DOI":"10.1109\/TNNLS.2020.3042508","article-title":"Model-free reinforcement learning for fully cooperative consensus problem of nonlinear multiagent systems","volume":"33","author":"Wang","year":"2022","journal-title":"IEEE Trans. Neural Netw. Learn. Syst."},{"issue":"1","key":"10.1016\/j.neucom.2026.133923_bib0060","doi-asserted-by":"crossref","first-page":"1548","DOI":"10.1109\/JSYST.2022.3203979","article-title":"Fully distributed optimal consensus for a class of second-order nonlinear multiagent systems with switching topologies","volume":"17","author":"Zou","year":"2023","journal-title":"IEEE Syst. J."},{"issue":"8","key":"10.1016\/j.neucom.2026.133923_bib0065","doi-asserted-by":"crossref","first-page":"4741","DOI":"10.1109\/TSMC.2019.2944259","article-title":"Nearly optimal integral sliding-mode consensus control for multiagent systems with disturbances","volume":"51","author":"Zhang","year":"2021","journal-title":"IEEE Trans. Syst. Man, Cybern. Syst."},{"issue":"7","key":"10.1016\/j.neucom.2026.133923_bib0070","doi-asserted-by":"crossref","first-page":"1701","DOI":"10.1109\/TSMC.2017.2668440","article-title":"Predictive suboptimal consensus of multiagent systems with nonlinear dynamics","volume":"47","author":"Zhang","year":"2017","journal-title":"IEEE Trans. Syst. Man, Cybern. Syst."},{"key":"10.1016\/j.neucom.2026.133923_bib0075","doi-asserted-by":"crossref","first-page":"426","DOI":"10.1016\/j.automatica.2017.08.010","article-title":"Adaptive near-optimal consensus of high-order nonlinear multi-agent systems with heterogeneity","volume":"85","author":"Zhang","year":"2017","journal-title":"Automatica"},{"issue":"2","key":"10.1016\/j.neucom.2026.133923_bib0080","doi-asserted-by":"crossref","first-page":"534","DOI":"10.1109\/72.839023","article-title":"On equilibria, stability, and instability of hopfield neural networks","volume":"11","author":"Guan","year":"2000","journal-title":"IEEE Trans. Neural Netw."},{"issue":"3","key":"10.1016\/j.neucom.2026.133923_bib0085","doi-asserted-by":"crossref","first-page":"1098","DOI":"10.1109\/TNNLS.2021.3105519","article-title":"An overview of the stability analysis of recurrent neural networks with multiple equilibria","volume":"34","author":"Liu","year":"2023","journal-title":"IEEE Trans. Neural Netw. Learn. Syst."},{"issue":"1","key":"10.1016\/j.neucom.2026.133923_bib0090","doi-asserted-by":"crossref","first-page":"1213","DOI":"10.1109\/TNNLS.2023.3334871","article-title":"Multistability of state-dependent switched fractional-order hopfield neural networks with Mexican-hat activation function and its application in associative memories","volume":"36","author":"Cao","year":"2025","journal-title":"IEEE Trans. Neural Netw. Learn. Syst."},{"issue":"3","key":"10.1016\/j.neucom.2026.133923_bib0095","doi-asserted-by":"crossref","first-page":"821","DOI":"10.1109\/TVLSI.2024.3480958","article-title":"A programmable and reconfigurable CMOS analog hopfield network for NP-hard problems","volume":"33","author":"Mathews","year":"2025","journal-title":"IEEE Trans. VLSI Syst."},{"issue":"4","key":"10.1016\/j.neucom.2026.133923_bib0100","doi-asserted-by":"crossref","first-page":"2677","DOI":"10.1109\/TETCI.2024.3369667","article-title":"A survey of neurodynamic optimization","volume":"8","author":"Xia","year":"2024","journal-title":"IEEE Trans. Emerg. Topics Comput. Intell."},{"issue":"7","key":"10.1016\/j.neucom.2026.133923_bib0105","doi-asserted-by":"crossref","first-page":"4368","DOI":"10.1109\/TAC.2023.3319132","article-title":"Low-computational-complexity zeroing neural network model for solving systems of dynamic nonlinear equations","volume":"69","author":"Zheng","year":"2024","journal-title":"IEEE Trans. Autom. Control"},{"issue":"1","key":"10.1016\/j.neucom.2026.133923_bib0110","doi-asserted-by":"crossref","first-page":"559","DOI":"10.1109\/TNNLS.2022.3175899","article-title":"GNN model for time-varying matrix inversion with robust finite-time convergence","volume":"35","author":"Zhang","year":"2024","journal-title":"IEEE Trans. Neural Netw. Learn. Syst."},{"issue":"8","key":"10.1016\/j.neucom.2026.133923_bib0115","doi-asserted-by":"crossref","first-page":"4786","DOI":"10.1109\/TSMC.2024.3387023","article-title":"GNN model with robust finite-time convergence for time-varying systems of linear equations","volume":"54","author":"Zhang","year":"2024","journal-title":"IEEE Trans. Syst. Man Cybern. Syst."},{"issue":"4","key":"10.1016\/j.neucom.2026.133923_bib0120","doi-asserted-by":"crossref","first-page":"1009","DOI":"10.1109\/JAS.2023.123132","article-title":"Kinematic control of serial manipulators under false data injection attack","volume":"10","author":"Zhang","year":"2023","journal-title":"IEEE\/CAA J. Autom. Sinica"},{"issue":"6","key":"10.1016\/j.neucom.2026.133923_bib0125","doi-asserted-by":"crossref","first-page":"11189","DOI":"10.1109\/TNNLS.2024.3466296","article-title":"Neural dynamic fault-tolerant scheme for collaborative motion planning of dual-redundant robot manipulators","volume":"36","author":"Zhang","year":"2025","journal-title":"IEEE Trans. Neural Netw. Learn. Syst."},{"issue":"6","key":"10.1016\/j.neucom.2026.133923_bib0130","doi-asserted-by":"crossref","first-page":"6124","DOI":"10.1109\/TIE.2024.3482112","article-title":"A triple-integral noise-resistant RNN for time-dependent constrained nonlinear optimization applied to manipulator control","volume":"72","author":"Han","year":"2025","journal-title":"IEEE Trans. Ind. Electron."},{"issue":"8","key":"10.1016\/j.neucom.2026.133923_bib0135","doi-asserted-by":"crossref","first-page":"1747","DOI":"10.1109\/TNNLS.2016.2549566","article-title":"A collective neurodynamic approach to distributed constrained optimization","volume":"28","author":"Liu","year":"2017","journal-title":"IEEE Trans. Neural Netw. Learn. Syst."},{"issue":"5","key":"10.1016\/j.neucom.2026.133923_bib0140","doi-asserted-by":"crossref","first-page":"3141","DOI":"10.1109\/TSMC.2022.3221937","article-title":"A collaborative neurodynamic approach to distributed global optimization","volume":"53","author":"Xia","year":"2023","journal-title":"IEEE Trans. Syst. Man Cybern. Syst."},{"issue":"8","key":"10.1016\/j.neucom.2026.133923_bib0145","doi-asserted-by":"crossref","first-page":"10031","DOI":"10.1109\/TII.2024.3383508","article-title":"A neurodynamic approach for solving time-dependent nonlinear equation system: a distributed optimization perspective","volume":"20","author":"Li","year":"2024","journal-title":"IEEE Trans. Ind. Inform."},{"issue":"2","key":"10.1016\/j.neucom.2026.133923_bib0150","doi-asserted-by":"crossref","first-page":"1288","DOI":"10.1109\/TSMC.2019.2896958","article-title":"Intelligent leader-following consensus formation control using recurrent neural networks for small-size unmanned helicopters","volume":"51","author":"Kuo","year":"2021","journal-title":"IEEE Trans. Syst. Man, Cybern. Syst."},{"key":"10.1016\/j.neucom.2026.133923_bib0155","series-title":"ICASSP 2025 - IEEE Int. Conf. Acoust","first-page":"1","article-title":"Distributed recurrent neural network for multi-agent consensus control","author":"Li","year":"2025"},{"issue":"12","key":"10.1016\/j.neucom.2026.133923_bib0160","doi-asserted-by":"crossref","first-page":"18394","DOI":"10.1109\/TNNLS.2023.3315332","article-title":"A dynamic gain fixed-time robust ZNN model for time-variant equality constrained quaternion least squares problem with applications to multiagent systems","volume":"35","author":"Cao","year":"2024","journal-title":"IEEE Trans. Neural Netw. Learn. Syst."},{"key":"10.1016\/j.neucom.2026.133923_bib0165","doi-asserted-by":"crossref","DOI":"10.1016\/j.automatica.2022.110531","article-title":"Secure and collision-free multi-platoon control of automated vehicles under data falsification attacks","volume":"145","author":"Xiao","year":"2022","journal-title":"Automatica"},{"issue":"4","key":"10.1016\/j.neucom.2026.133923_bib0170","first-page":"6302","article-title":"Reinforcement learning based optimized sliding-mode consensus control of high-order nonlinear canonical dynamic multiagent system","volume":"17","author":"Li","year":"2023","journal-title":"IEEE Syst. J."},{"issue":"11","key":"10.1016\/j.neucom.2026.133923_bib0175","doi-asserted-by":"crossref","first-page":"6399","DOI":"10.1109\/TFUZZ.2024.3449324","article-title":"Fuzzy adaptive exact-optimal consensus output-feedback control for uncertain nonlinear high-order multiagent systems","volume":"32","author":"Cui","year":"2024","journal-title":"IEEE Trans. Fuzzy Syst."},{"key":"10.1016\/j.neucom.2026.133923_bib0180","doi-asserted-by":"crossref","first-page":"4206","DOI":"10.1109\/TASE.2024.3408650","article-title":"Event-based distributed bipartite consensus of high-order nonlinear multi-agent network: applications to hypersonic flight vehicles","volume":"22","author":"Lv","year":"2025","journal-title":"IEEE Trans. Autom. Sci. Eng."},{"issue":"6","key":"10.1016\/j.neucom.2026.133923_bib0185","doi-asserted-by":"crossref","first-page":"6219","DOI":"10.1109\/TIE.2022.3198255","article-title":"Recurrent neural network-based robust adaptive model predictive speed control for PMSM with parameter mismatch","volume":"70","author":"Nguyen","year":"2023","journal-title":"IEEE Trans. Ind. Electron."},{"key":"10.1016\/j.neucom.2026.133923_bib0190","doi-asserted-by":"crossref","first-page":"1677","DOI":"10.1002\/rnc.3626","article-title":"Adaptive stationary consensus protocol for a class of high-order nonlinear multiagent systems with jointly connected topologies","volume":"27","author":"Rezaee","year":"2017","journal-title":"Int. J. Robust Nonlinear Control"},{"issue":"2","key":"10.1016\/j.neucom.2026.133923_bib0195","doi-asserted-by":"crossref","first-page":"426","DOI":"10.1109\/TNN.2003.809409","article-title":"Exponential stability of globally projected dynamic systems","volume":"14","author":"Gao","year":"2003","journal-title":"IEEE Trans. Neural Netw."},{"key":"10.1016\/j.neucom.2026.133923_bib0200","series-title":"Nonlinear Control Systems: An Introduction","author":"Isidori","year":"1995"},{"issue":"2","key":"10.1016\/j.neucom.2026.133923_bib0205","doi-asserted-by":"crossref","first-page":"1131","DOI":"10.1109\/TNSE.2022.3229752","article-title":"Bipartite tracking consensus for high-order heterogeneous uncertain nonlinear multi-agent systems with unknown leader dynamics via adaptive fully-distributed PID control","volume":"10","author":"Lui","year":"2023","journal-title":"IEEE Trans. Netw. Sci. Eng."},{"issue":"13","key":"10.1016\/j.neucom.2026.133923_bib0210","doi-asserted-by":"crossref","first-page":"3117","DOI":"10.1080\/00207721.2025.2492301","article-title":"H\u221e consensus control for high-order fully actuated multi-agent systems with external disturbances","volume":"56","author":"Zhang","year":"2025","journal-title":"Int. J. Syst. Sci."},{"issue":"11","key":"10.1016\/j.neucom.2026.133923_bib0215","doi-asserted-by":"crossref","first-page":"6012","DOI":"10.1109\/TFUZZ.2024.3418772","article-title":"Flexible prescribed performance output feedback control for nonlinear systems with input saturation","volume":"32","author":"Yao","year":"2024","journal-title":"IEEE Trans. Fuzzy Syst."},{"issue":"4","key":"10.1016\/j.neucom.2026.133923_bib0220","doi-asserted-by":"crossref","first-page":"1241","DOI":"10.1109\/TFUZZ.2024.3516132","article-title":"Sliding flexible prescribed performance control for input saturated nonlinear systems","volume":"33","author":"Yao","year":"2025","journal-title":"IEEE Trans. Fuzzy Syst."},{"issue":"2","key":"10.1016\/j.neucom.2026.133923_bib0225","doi-asserted-by":"crossref","first-page":"968","DOI":"10.1109\/TCYB.2025.3610913","article-title":"Sliding flexible prescribed performance boundary-guided reinforcement learning control for input-constrained nonlinear systems","volume":"56","author":"Yao","year":"2026","journal-title":"IEEE Trans. Cybern."},{"key":"10.1016\/j.neucom.2026.133923_bib0230","first-page":"689","article-title":"Asynchronous distributed model predictive control for optimal output consensus of high-order multi-agent systems","volume":"7","author":"Li","year":"2021","journal-title":"IEEE Trans. Signal Inf. Process."},{"issue":"9","key":"10.1016\/j.neucom.2026.133923_bib0235","doi-asserted-by":"crossref","first-page":"5546","DOI":"10.1109\/TSMC.2021.3130070","article-title":"Optimized leader-follower consensus control using reinforcement learning for a class of second-order nonlinear multiagent systems","volume":"52","author":"Wen","year":"2022","journal-title":"IEEE Trans. Syst. Man Cybern. Syst."}],"container-title":["Neurocomputing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0925231226013202?httpAccept=text\/xml","content-type":"text\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0925231226013202?httpAccept=text\/plain","content-type":"text\/plain","content-version":"vor","intended-application":"text-mining"}],"deposited":{"date-parts":[[2026,8,27]],"date-time":"2026-08-27T16:20:05Z","timestamp":1787847605000},"score":1,"resource":{"primary":{"URL":"https:\/\/linkinghub.elsevier.com\/retrieve\/pii\/S0925231226013202"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,9]]},"references-count":47,"alternative-id":["S0925231226013202"],"URL":"https:\/\/doi.org\/10.1016\/j.neucom.2026.133923","relation":{},"ISSN":["0925-2312"],"issn-type":[{"value":"0925-2312","type":"print"}],"subject":[],"published":{"date-parts":[[2026,9]]},"assertion":[{"value":"Elsevier","name":"publisher","label":"This article is maintained by"},{"value":"RNN-based optimal consensus of high-order heterogeneous nonlinear MAS with input constraints","name":"articletitle","label":"Article Title"},{"value":"Neurocomputing","name":"journaltitle","label":"Journal Title"},{"value":"https:\/\/doi.org\/10.1016\/j.neucom.2026.133923","name":"articlelink","label":"CrossRef DOI link to publisher maintained version"},{"value":"article","name":"content_type","label":"Content Type"},{"value":"\u00a9 2026 Elsevier B.V. All rights are reserved, including those for text and data mining, AI training, and similar technologies.","name":"copyright","label":"Copyright"}],"article-number":"133923"}}