{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,9]],"date-time":"2026-06-09T05:33:38Z","timestamp":1780983218432,"version":"3.54.1"},"reference-count":39,"publisher":"Springer Science and Business Media LLC","issue":"2","license":[{"start":{"date-parts":[[2022,1,18]],"date-time":"2022-01-18T00:00:00Z","timestamp":1642464000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2022,1,18]],"date-time":"2022-01-18T00:00:00Z","timestamp":1642464000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"}],"funder":[{"name":"Natural Science Foundation Project of Chongqing CSTC","award":["cstc2019jcyj-msxm2319"],"award-info":[{"award-number":["cstc2019jcyj-msxm2319"]}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Cogn Comput"],"published-print":{"date-parts":[[2022,3]]},"DOI":"10.1007\/s12559-021-09959-x","type":"journal-article","created":{"date-parts":[[2022,1,18]],"date-time":"2022-01-18T09:17:50Z","timestamp":1642497470000},"page":"814-827","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":13,"title":["Observer and Command-Filter-Based Adaptive Neural Network Control Algorithms for Nonlinear Multi-agent Systems with Input Delay"],"prefix":"10.1007","volume":"14","author":[{"given":"Lidan","family":"Ma","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8893-5430","authenticated-orcid":false,"given":"Xin","family":"Wang","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yuhao","family":"Zhou","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2022,1,18]]},"reference":[{"issue":"6","key":"9959_CR1","doi-asserted-by":"publisher","first-page":"1216","DOI":"10.1007\/s12555-013-0492-z","volume":"12","author":"H Chen","year":"2014","unstructured":"Chen H. Robust stabilization for a class of dynamic feedback uncertain nonholonomic mobile robots with input saturation. Int J Control Autom Syst. 2014;12(6):1216\u201324.","journal-title":"Int. J. Control Autom. Syst."},{"issue":"2","key":"9959_CR2","doi-asserted-by":"publisher","first-page":"296","DOI":"10.1109\/JSEE.2013.00037","volume":"24","author":"X Wang","year":"2013","unstructured":"Wang X, Wu J, Wang X. Distributed attitude consensus of spacecraft formation flying. J Syst Engin Elec. 2013;24(2):296\u2013302.","journal-title":"J. Syst. Engin. Elec."},{"key":"9959_CR3","doi-asserted-by":"publisher","first-page":"130","DOI":"10.1016\/j.sigpro.2019.01.020","volume":"159","author":"MR Leonard","year":"2019","unstructured":"Leonard MR, Zoubir AM. Multi-target tracking in distributed sensor networks using particle PHD filters. Signal Process. 2019;159:130\u201346.","journal-title":"Signal Process."},{"issue":"17","key":"9959_CR4","doi-asserted-by":"publisher","first-page":"12180","DOI":"10.1016\/j.jfranklin.2020.08.044","volume":"357","author":"W Ao","year":"2020","unstructured":"Ao W, Huang J, Xue F. Adaptive leaderless consensus control of a class of strict-feedback nonlinear multi-agent systems with unknown control directions: A non-Nussbaum function based approach. J Frankl Inst. 2020;357(17):12180\u201396.","journal-title":"J. Frankl. Inst."},{"key":"9959_CR5","doi-asserted-by":"publisher","first-page":"116","DOI":"10.1016\/j.isatra.2016.07.011","volume":"65","author":"W Guo","year":"2016","unstructured":"Guo W. Leader-following consensus of the second-order multi-agent systems under directed topology. ISA Trans. 2016;65:116\u201324.","journal-title":"ISA Trans."},{"key":"9959_CR6","doi-asserted-by":"publisher","first-page":"70799","DOI":"10.1109\/ACCESS.2019.2919708","volume":"7","author":"Q Yang","year":"2019","unstructured":"Yang Q, Li J, Wang B. Leader-following output consensus for high-order nonlinear multi-agent systems by distributed event-triggered strategy via sampled data information. IEEE Access. 2019;7:70799\u2013810.","journal-title":"IEEE Access."},{"key":"9959_CR7","doi-asserted-by":"crossref","unstructured":"Yang Y, Xu H, Yue D. Observer-based distributed secure consensus control of a class of linear multi-agent systems subject to random attacks. IEEE Trans. Circuits Syst. I, Reg. Papers. 2019;66(8):3089\u20133099.","DOI":"10.1109\/TCSI.2019.2904747"},{"issue":"3","key":"9959_CR8","doi-asserted-by":"publisher","first-page":"1010","DOI":"10.1109\/TNNLS.2019.2915376","volume":"31","author":"QK Shen","year":"2020","unstructured":"Shen QK, Shi P, Zhu JW, Wang SY, Shi Y. Neural networks-based distributed adaptive control of nonlinear multiagent systems. IEEE Trans Neural Netw Learn Syst. 2020;31(3):1010\u201321.","journal-title":"IEEE Trans. Neural. Netw. Learn. Syst."},{"issue":"3","key":"9959_CR9","doi-asserted-by":"publisher","first-page":"987","DOI":"10.1109\/TMECH.2013.2265312","volume":"19","author":"KK Ahn","year":"2014","unstructured":"Ahn KK, Nam DNC, Jin M. Adaptive backstepping control of an electrohydraulic actuator. IEEE\/ASME Trans Mechatron. 2014;19(3):987\u201395.","journal-title":"IEEE\/ASME Trans. Mechatron."},{"key":"9959_CR10","doi-asserted-by":"publisher","first-page":"134","DOI":"10.1016\/j.sysconle.2018.11.007","volume":"123","author":"F Mazenc","year":"2019","unstructured":"Mazenc F, Burlio L, Malisoff M. Backstepping design for output feedback stabilization for a class of uncertain systems. Systems Control Lett. 2019;123:134\u201343.","journal-title":"Systems Control Lett."},{"key":"9959_CR11","doi-asserted-by":"crossref","unstructured":"Ma L, Liu L. Adaptive neural network control design for uncertain nonstrict feedback nonlinear system with state constraints. IEEE Trans Syst Man Cybern Syst. 2021;51(6):3678\u20133686.","DOI":"10.1109\/TSMC.2019.2922393"},{"issue":"7","key":"9959_CR12","doi-asserted-by":"publisher","first-page":"2593","DOI":"10.1002\/rnc.4887","volume":"30","author":"MM Polycarpou","year":"2020","unstructured":"Polycarpou MM. Adaptive neural network tracking control for uncertain nonlinear systems with input delay and saturation. Int J Robust Nonlin. 2020;30(7):2593\u2013610.","journal-title":"Int. J. Robust Nonlin."},{"issue":"1","key":"9959_CR13","doi-asserted-by":"publisher","first-page":"2249","DOI":"10.1007\/s11071-020-05885-z","volume":"101","author":"D Yao","year":"2020","unstructured":"Yao D, Yue D, Zhao N, Zhang T. Adaptive neural network consensus tracking control for uncertain multi-agent systems with predefined accuracy. Nonlinear Dyn. 2020;101(1):2249\u201362.","journal-title":"Nonlinear Dyn."},{"issue":"10","key":"9959_CR14","doi-asserted-by":"publisher","first-page":"1893","DOI":"10.1109\/TAC.2000.880994","volume":"45","author":"D Swaroop","year":"2002","unstructured":"Swaroop D, Hedrick JK, Yip PP, Gerdes JC. Dynamic surface control for a class of nonlinear systems. IEEE Trans Autom Control. 2002;45(10):1893\u20139.","journal-title":"IEEE Trans. Autom. Control"},{"issue":"9","key":"9959_CR15","doi-asserted-by":"publisher","first-page":"2156","DOI":"10.1109\/TNNLS.2016.2577342","volume":"28","author":"Z Peng","year":"2017","unstructured":"Peng Z, Dan W, Wang J. Neural network-based adaptive dynamic surface control for a class of uncertain nonlinear systems in strict-feedback form. IEEE Trans Neural Netw. 2017;28(9):2156\u201367.","journal-title":"IEEE Trans. Neural Netw."},{"issue":"4","key":"9959_CR16","doi-asserted-by":"publisher","first-page":"666","DOI":"10.1109\/TNNLS.2013.2238554","volume":"24","author":"SJ Yoo","year":"2013","unstructured":"Yoo SJ. Distributed consensus tracking for multiple uncertain nonlinear strict-feedback systems under a directed graph. IEEE Trans Neural Netw Learn Syst. 2013;24(4):666\u201372.","journal-title":"IEEE Trans. Neural Netw. Learn. Syst."},{"issue":"1","key":"9959_CR17","doi-asserted-by":"publisher","first-page":"169","DOI":"10.1109\/JAS.2017.7510382","volume":"5","author":"Y Yang","year":"2018","unstructured":"Yang Y, Yue D. Distributed tracking control of a class of multi-agent systems in non-affine pure-feedback form under a directed topology. IEEE\/CAA J Autom Sinica. 2018;5(1):169\u201380.","journal-title":"IEEE\/CAA J. Autom. Sinica"},{"issue":"6","key":"9959_CR18","doi-asserted-by":"publisher","first-page":"1391","DOI":"10.1109\/TAC.2009.2015562","volume":"54","author":"JA Farrell","year":"2009","unstructured":"Farrell JA, Polycarpou M, Sharma M, Dong W. Command filtered backstepping. IEEE Trans Autom Control. 2009;54(6):1391\u20135.","journal-title":"IEEE Trans. Autom. Control"},{"issue":"9","key":"9959_CR19","doi-asserted-by":"publisher","first-page":"5962","DOI":"10.1109\/TIE.2015.2418317","volume":"62","author":"JP Yu","year":"2015","unstructured":"Yu JP, Shi P, Dong WJ, Yu HS. Observer and command-filter-based adaptive fuzzy output feedback control of uncertain nonlinear systems. IEEE Trans Ind Electron. 2015;62(9):5962\u201370.","journal-title":"IEEE Trans. Ind. Electron."},{"key":"9959_CR20","doi-asserted-by":"crossref","unstructured":"Zhang J, Li S, Ahn CK, Xiang Z. Decentralized event-triggered adaptive fuzzy control for nonlinear switched large-scale systems with input delay via command-filtered backstepping. IEEE Trans Fuzzy Syst. 2021;29(10).","DOI":"10.1109\/TFUZZ.2021.3066297"},{"key":"9959_CR21","doi-asserted-by":"publisher","first-page":"120","DOI":"10.1016\/j.automatica.2014.12.046","volume":"53","author":"QK Shen","year":"2015","unstructured":"Shen QK, Shi P. Distributed command filtered backstepping consensus tracking control of nonlinear multiple-agent systems in strict-feedback form. Automatica. 2015;53:120\u20134.","journal-title":"Automatica"},{"issue":"5","key":"9959_CR22","doi-asserted-by":"publisher","first-page":"509","DOI":"10.1049\/iet-cta.2015.0627","volume":"10","author":"G Cui","year":"2016","unstructured":"Cui G, Xu S, Lewis FL, Zhang B, Ma Q. Distributed consensus tracking for non-linear multi-agent systems with input saturation: A command filtered backstepping approach. IET Control Theory Appl. 2016;10(5):509\u201316.","journal-title":"IET Control Theory Appl."},{"key":"9959_CR23","doi-asserted-by":"crossref","unstructured":"Cui G, Yu J, Song G. Distributed consensus control for second-order stochastic nonlinear multiagent systems using command filter backstepping. 2018 5th International Conference on Information, Cybernetics, and Computational Social Systems (ICCSS). 2018;105\u2013110.","DOI":"10.1109\/ICCSS.2018.8572405"},{"key":"9959_CR24","doi-asserted-by":"publisher","first-page":"17","DOI":"10.1016\/j.ins.2021.02.078","volume":"565","author":"Y Cui","year":"2021","unstructured":"Cui Y, Liu XP, Deng X, Wen GX. Command-filter-based adaptive finite-time consensus control for nonlinear strict-feedback multi-agent systems with dynamic leader. Inf Sci. 2021;565:17\u201331.","journal-title":"Inf. Sci."},{"key":"9959_CR25","doi-asserted-by":"crossref","unstructured":"Tong SC, Li YM, Gang F, Li TS. Observer-based adaptive fuzzy backstepping dynamic surface control for a class of MIMO nonlinear systems. IEEE Trans Syst Man Cybern B Cybern.\u00a02011;41(4):1124\u20131135.","DOI":"10.1109\/TSMCB.2011.2108283"},{"issue":"7","key":"9959_CR26","doi-asserted-by":"publisher","first-page":"1591","DOI":"10.1109\/TCYB.2015.2452217","volume":"46","author":"CLP Chen","year":"2017","unstructured":"Chen CLP, Wen G-X, Liu Y-J, Liu Z. Observer-based adaptive backstepping consensus tracking control for high-order nonlinear semi-strict-feedback multiagent systems. IEEE Trans Cybern. 2017;46(7):1591\u2013601.","journal-title":"IEEE Trans. Cybern."},{"issue":"9","key":"9959_CR27","doi-asserted-by":"publisher","first-page":"2568","DOI":"10.1109\/TCYB.2017.2655501","volume":"47","author":"H Wang","year":"2017","unstructured":"Wang H, Liu PX, Shi P. Observer-based fuzzy adaptive output-feedback control of stochastic nonlinear multiple time-delay systems. IEEE Trans Cybern. 2017;47(9):2568\u201378.","journal-title":"IEEE Trans. Cybern."},{"issue":"3","key":"9959_CR28","first-page":"195","volume":"63","author":"WB Xiao","year":"2020","unstructured":"Xiao WB, Cao L, Li HY, Lu RQ. Observer-based adaptive consensus control for nonlinear multi-agent systems with time-delay. Inf Sci. 2020;63(3):195\u2013211.","journal-title":"Inf. Sci."},{"key":"9959_CR29","doi-asserted-by":"publisher","first-page":"221","DOI":"10.1016\/j.neucom.2014.05.039","volume":"145","author":"G Sun","year":"2014","unstructured":"Sun G, Wang D, Wang M. Robust adaptive neural network control of a class of uncertain strict-feedback nonlinear systems with unknown dead-zone and disturbances. Neurocomputing. 2014;145:221\u20139.","journal-title":"Neurocomputing"},{"key":"9959_CR30","doi-asserted-by":"crossref","unstructured":"Zhou Q, Li H, Wu C, Wang L, Ahn CK. Adaptive fuzzy control of nonlinear systems with unmodeled dynamics and input saturation using small-gain approach. IEEE Trans Syst Man Cybern Syst. 2017;47(8):1979-1989.","DOI":"10.1109\/TSMC.2016.2586108"},{"issue":"2","key":"9959_CR31","doi-asserted-by":"publisher","first-page":"701","DOI":"10.1109\/TCST.2017.2670522","volume":"26","author":"RC Avram","year":"2018","unstructured":"Avram RC, Zhang X, Muse J. Nonlinear adaptive fault-tolerant quadrotor altitude and attitude tracking with multiple actuator faults. IEEE Trans Control Syst Technol. 2018;26(2):701\u20137.","journal-title":"IEEE Trans. Control Syst. Technol."},{"issue":"4","key":"9959_CR32","doi-asserted-by":"publisher","first-page":"716","DOI":"10.1109\/TCNS.2016.2545860","volume":"4","author":"C Wang","year":"2017","unstructured":"Wang C, Zuo Z, Lin Z, Ding Z. A truncated prediction approach to consensus control of lipschitz nonlinear multi-agent systems with input delay. IEEE Trans Control Netw Syst. 2017;4(4):716\u201324.","journal-title":"IEEE Trans. Control Netw. Syst."},{"issue":"1","key":"9959_CR33","first-page":"126","volume":"51","author":"L Li","year":"2021","unstructured":"Li L, Niu B. Adaptive neural network tracking control for a class of switched strict-feedback nonlinear systems with input delay. Neurocomputing. 2021;51(1):126\u201337.","journal-title":"Neurocomputing"},{"key":"9959_CR34","first-page":"2121","volume":"173","author":"Q Zhang","year":"2016","unstructured":"Zhang Q, He D. Disturbance-observer-based adaptive fuzzy control for strict-feedback switched nonlinear systems with input delay. IEEE Trans Fuzzy Syst. 2016;173:2121\u20138.","journal-title":"IEEE Trans. Fuzzy Syst."},{"key":"9959_CR35","doi-asserted-by":"publisher","first-page":"2707","DOI":"10.1007\/s11071-019-04954-2","volume":"96","author":"W Wang","year":"2019","unstructured":"Wang W, Liang H, Zhang Y, Li T. Adaptive cooperative control for a class of nonlinear multi-agent systems with dead zone and input delay. Nonlinear Dyn. 2019;96:2707\u201319.","journal-title":"Nonlinear Dyn."},{"issue":"19","key":"9959_CR36","doi-asserted-by":"publisher","first-page":"2755","DOI":"10.1016\/j.fss.2009.03.008","volume":"160","author":"S Tong","year":"2009","unstructured":"Tong S, Li C, Li Y. Fuzzy adaptive observer backstepping control for MIMO nonlinear systems. Fuzzy Sets Syst. 2009;160(19):2755\u201375.","journal-title":"Fuzzy Sets Syst."},{"issue":"3","key":"9959_CR37","doi-asserted-by":"publisher","first-page":"566","DOI":"10.1109\/TCST.2011.2121907","volume":"20","author":"W Dong","year":"2012","unstructured":"Dong W, Farrell JA, Polycarpou M, Djapic V, Sharma M. Command filtered adaptive backstepping. IEEE Trans Control Syst Technol. 2012;20(3):566\u201380.","journal-title":"IEEE Trans. Control Syst. Technol."},{"issue":"7","key":"9959_CR38","doi-asserted-by":"publisher","first-page":"1432","DOI":"10.1016\/j.automatica.2012.05.008","volume":"48","author":"H Zhang","year":"2012","unstructured":"Zhang H, Lewis FL. Adaptive cooperative tracking control of higher-order nonlinear systems with unknown dynamics. Automatica. 2012;48(7):1432\u20139.","journal-title":"Automatica"},{"issue":"6","key":"9959_CR39","first-page":"1","volume":"30","author":"S Shuai","year":"2018","unstructured":"Shuai S, Tong S. Observer-based adaptive fuzzy quantized tracking DSC design for MIMO nonstrict-feedback nonlinear systems. Neural Comput Appl. 2018;30(6):1\u201311.","journal-title":"Neural Comput. Appl."}],"container-title":["Cognitive Computation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s12559-021-09959-x.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s12559-021-09959-x\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s12559-021-09959-x.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,4,18]],"date-time":"2022-04-18T09:33:46Z","timestamp":1650274426000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s12559-021-09959-x"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,1,18]]},"references-count":39,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2022,3]]}},"alternative-id":["9959"],"URL":"https:\/\/doi.org\/10.1007\/s12559-021-09959-x","relation":{},"ISSN":["1866-9956","1866-9964"],"issn-type":[{"value":"1866-9956","type":"print"},{"value":"1866-9964","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,1,18]]},"assertion":[{"value":"12 August 2021","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"30 October 2021","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"18 January 2022","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 conflict of interest","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of Interest"}},{"value":"This article does not contain any studies with human participants or animals per-formed by any of the authors.","order":3,"name":"Ethics","group":{"name":"EthicsHeading","label":"Ethical Approval"}}]}}