{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,19]],"date-time":"2026-02-19T00:08:16Z","timestamp":1771459696638,"version":"3.50.1"},"reference-count":40,"publisher":"Oxford University Press (OUP)","issue":"2","license":[{"start":{"date-parts":[[2019,4,23]],"date-time":"2019-04-23T00:00:00Z","timestamp":1555977600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/academic.oup.com\/journals\/pages\/open_access\/funder_policies\/chorus\/standard_publication_model"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["61374104"],"award-info":[{"award-number":["61374104"]}],"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":["61773170"],"award-info":[{"award-number":["61773170"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100003453","name":"Natural Science Foundation of Guangdong Province","doi-asserted-by":"publisher","award":["2016A030313505"],"award-info":[{"award-number":["2016A030313505"]}],"id":[{"id":"10.13039\/501100003453","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2020,6,6]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>In this paper, the iterative learning control technique is applied for singular multi-agent systems to perform consensus tracking. Here, the communication among the followers is described by a directed graph, and only a portion of the followers can receive the leader\u2019s information. Based on the equivalent restrict decomposition form of singular agents, a unified distributed learning algorithm is proposed in both continuous-time domain and discrete-time domain. Furthermore, the convergence condition of the algorithm is presented and analyzed. It is shown that the algorithm can guarantee the states of the followers converge to the leader\u2019s trajectory on a finite time interval along the iteration axis. Finally, two simulation examples are given to illustrate the effectiveness of the theoretical results.<\/jats:p>","DOI":"10.1093\/imamci\/dnz012","type":"journal-article","created":{"date-parts":[[2019,4,23]],"date-time":"2019-04-23T07:23:21Z","timestamp":1556004201000},"page":"535-558","source":"Crossref","is-referenced-by-count":13,"title":["Consensus control of singular multi-agent systems based on iterative learning approach"],"prefix":"10.1093","volume":"37","author":[{"given":"Panpan","family":"Gu","sequence":"first","affiliation":[{"name":"School of Automation Science and Engineering, South China University of Technology, Guangzhou, China"}]},{"given":"Senping","family":"Tian","sequence":"additional","affiliation":[{"name":"School of Automation Science and Engineering, South China University of Technology, Guangzhou, China"}]}],"member":"286","published-online":{"date-parts":[[2019,4,23]]},"reference":[{"key":"2020091709242425200_ref1","first-page":"3111","volume-title":"Iterative learning control for multi-agent formation. Proceedings of the ICROS-SICE International Joint Conference","author":"Ahn","year":"2009"},{"key":"2020091709242425200_ref2","doi-asserted-by":"crossref","first-page":"1655","DOI":"10.1002\/rnc.1538","article-title":"Trajectory-keeping in satellite formation flying via robust periodic learning control","volume":"20","author":"Ahn","year":"2010","journal-title":"Internat. J. Robust Nonlinear Control"},{"key":"2020091709242425200_ref3","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4615-5629-9","volume-title":"Iterative Learning Control: Analysis, Design, Integration and Applications","author":"Bien","year":"1998"},{"key":"2020091709242425200_ref4","doi-asserted-by":"crossref","first-page":"409","DOI":"10.1109\/TAC.2013.2283742","article-title":"Network clock synchronization based on the second-order linear consensus algorithm","volume":"59","author":"Carli","year":"2014","journal-title":"IEEE Trans. Automat. Control"},{"key":"2020091709242425200_ref5","first-page":"62","volume-title":"Stereo vision-based formation control of mobile robots using iterative learning. Proceedings of the International Conference on Humanized Systems","author":"Chen","year":"2010"},{"key":"2020091709242425200_ref6","doi-asserted-by":"crossref","DOI":"10.1007\/BFb0002475","volume-title":"Singular Control Systems. Lecture Notes in Control and Information Sciences","author":"Dai","year":"1989"},{"key":"2020091709242425200_ref7","doi-asserted-by":"crossref","first-page":"2881","DOI":"10.1016\/j.automatica.2013.06.014","article-title":"Consensus of second-order multi-agent systems via impulsive control using sampled hetero-information","volume":"49","author":"Ding","year":"2013","journal-title":"Automatica J. IFAC"},{"key":"2020091709242425200_ref8","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4419-6397-0","volume-title":"Analysis and Design of Descriptor Linear Systems","author":"Duan","year":"2010"},{"key":"2020091709242425200_ref9","doi-asserted-by":"crossref","first-page":"1465","DOI":"10.1109\/TAC.2004.834433","article-title":"Information flow and cooperative control of vehicle formations","volume":"49","author":"Fax","year":"2004","journal-title":"IEEE Trans. Automat. Control"},{"key":"2020091709242425200_ref10","doi-asserted-by":"crossref","first-page":"2621","DOI":"10.1007\/s11071-017-4035-7","article-title":"Consensus control for multi-agent systems with quasi-one-sided Lipschitz nonlinear dynamics via iterative learning algorithm","volume":"91","author":"Fu","year":"2018","journal-title":"Nonlinear Dynam."},{"key":"2020091709242425200_ref11","doi-asserted-by":"crossref","DOI":"10.1017\/CBO9780511810817","volume-title":"Matrix Analysis","author":"Horn","year":"1985"},{"key":"2020091709242425200_ref12","doi-asserted-by":"crossref","first-page":"109","DOI":"10.1049\/iet-cta.2008.0479","article-title":"Consensus control for multi-agent systems with double-integrator dynamics and time delays","volume":"4","author":"Hu","year":"2010","journal-title":"IET Control Theory Appl."},{"key":"2020091709242425200_ref13","first-page":"1044","article-title":"Iterative learning control approach for a kind of heterogeneous multi-agent systems with distributed initial state learning","volume":"265","author":"Li","year":"2015","journal-title":"Appl. Math. Comput."},{"key":"2020091709242425200_ref14","doi-asserted-by":"crossref","first-page":"1760","DOI":"10.1016\/j.automatica.2011.02.045","article-title":"Finite-time consensus algorithm for multi-agent systems with double-integrator dynamics","volume":"47","author":"Li","year":"2011","journal-title":"Automatica J. IFAC"},{"key":"2020091709242425200_ref15","doi-asserted-by":"crossref","first-page":"2397","DOI":"10.1007\/s11071-017-4020-1","article-title":"Finite-time consensus of nonlinear multi-agent system with prescribed performance","volume":"91","author":"Li","year":"2018","journal-title":"Nonlinear Dynam."},{"key":"2020091709242425200_ref16","doi-asserted-by":"crossref","first-page":"148","DOI":"10.1016\/j.sysconle.2011.10.011","article-title":"An iterative learning approach to formation control of multi-agent systems","volume":"61","author":"Liu","year":"2012","journal-title":"Syst. Control Lett."},{"key":"2020091709242425200_ref17","doi-asserted-by":"crossref","first-page":"625","DOI":"10.1080\/00207721.2013.793781","article-title":"Robust formation control of discrete-time multi-agent systems by iterative learning approach","volume":"46","author":"Liu","year":"2015","journal-title":"Int. J. Syst. Sci."},{"key":"2020091709242425200_ref18","doi-asserted-by":"crossref","first-page":"1152","DOI":"10.1109\/TAC.2014.2350391","article-title":"Designing fully distributed consensus protocols for linear multi-agent systems with directed graphs","volume":"60","author":"Li","year":"2015","journal-title":"IEEE Trans. Automat. Control"},{"key":"2020091709242425200_ref19","doi-asserted-by":"crossref","first-page":"991","DOI":"10.2307\/1912686","article-title":"Singular dynamic Leontief systems","volume":"45","author":"Luenberger","year":"1977","journal-title":"Econometrica"},{"key":"2020091709242425200_ref20","doi-asserted-by":"crossref","first-page":"5003","DOI":"10.1002\/mma.4948","article-title":"Learning formation control for fractional-order multiagent systems","volume":"41","author":"Luo","year":"2018","journal-title":"Math. Meth. Appl. Sci."},{"key":"2020091709242425200_ref21","doi-asserted-by":"crossref","first-page":"807","DOI":"10.1016\/j.sysconle.2012.04.007","article-title":"Tracking control over a finite interval for multi-agent systems with a time-varying reference trajectory","volume":"61","author":"Meng","year":"2012","journal-title":"Syst. Control Lett."},{"key":"2020091709242425200_ref22","doi-asserted-by":"crossref","first-page":"291","DOI":"10.1016\/j.automatica.2013.11.009","article-title":"On iterative learning algorithms for the formation control of nonlinear multi-agent systems","volume":"50","author":"Meng","year":"2014","journal-title":"Automatica J. IFAC"},{"key":"2020091709242425200_ref23","doi-asserted-by":"crossref","first-page":"1993","DOI":"10.1002\/rnc.3186","article-title":"High-precision formation control of nonlinear multi-agent systems with switching topologies: a learning approach","volume":"25","author":"Meng","year":"2015","journal-title":"Internat. J. Robust Nonlinear Control"},{"key":"2020091709242425200_ref24","doi-asserted-by":"crossref","first-page":"655","DOI":"10.1109\/TAC.2005.846556","article-title":"Consensus seeking in multiagent systems under dynamically changing interaction topologies","volume":"50","author":"Ren","year":"2005","journal-title":"IEEE Trans. Automat. Control"},{"key":"2020091709242425200_ref25","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-84800-015-5","volume-title":"Distributed Consensus in Multi-vehicle Cooperative Control","author":"Ren","year":"2008"},{"key":"2020091709242425200_ref26","doi-asserted-by":"crossref","first-page":"1443","DOI":"10.1016\/j.automatica.2011.02.014","article-title":"Spacecraft formation reconfiguration with collision avoidance","volume":"47","author":"Schlanbusch","year":"2011","journal-title":"Automatica J. IFAC"},{"key":"2020091709242425200_ref27","doi-asserted-by":"crossref","DOI":"10.1007\/978-981-10-8267-2","volume-title":"Iterative Learning Control with Passive Incomplete Information","author":"Shen","year":"2018"},{"key":"2020091709242425200_ref28","doi-asserted-by":"crossref","first-page":"2576","DOI":"10.1016\/j.jfranklin.2016.04.016","article-title":"Finite-time consensus problem of multi-agent systems with disturbance","volume":"353","author":"Sun","year":"2016","journal-title":"J. Franklin Inst. B"},{"key":"2020091709242425200_ref29","doi-asserted-by":"crossref","first-page":"96","DOI":"10.1109\/MCS.2006.1636313","article-title":"A survey of iterative learning control: a learning-based method for high-performance tracking control","volume":"26","author":"Tharayil","year":"2006","journal-title":"IEEE Control Syst. Mag."},{"key":"2020091709242425200_ref30","doi-asserted-by":"crossref","first-page":"950","DOI":"10.1109\/TAC.2010.2041610","article-title":"Finite-time consensus problems for networks of dynamic agents","volume":"55","author":"Wang","year":"2010","journal-title":"IEEE Trans. Autom. Control"},{"key":"2020091709242425200_ref31","doi-asserted-by":"crossref","first-page":"170","DOI":"10.1002\/rnc.1687","article-title":"Consensus in multi-agent systems with communication constraints","volume":"22","author":"Wen","year":"2012","journal-title":"Internat. J. Robust Nonlinear Control"},{"key":"2020091709242425200_ref32","doi-asserted-by":"crossref","first-page":"1531","DOI":"10.1109\/TCSI.2013.2289399","article-title":"Guaranteed-cost consensus for singular multi-agent systems with switching topologies","volume":"61","author":"Xi","year":"2014","journal-title":"IEEE Trans. Circuits Syst. I: Regul. Pap."},{"key":"2020091709242425200_ref33","doi-asserted-by":"crossref","first-page":"1666","DOI":"10.1016\/j.neucom.2015.07.108","article-title":"Group consensus of multi-agent systems with communication delays","volume":"171","author":"Xia","year":"2016","journal-title":"Neurocomputing"},{"key":"2020091709242425200_ref34","volume-title":"Linear and Nonlinear Iterative Learning Control, Lecture Notes in Control and Information Sciences","author":"Xu","year":"2003"},{"key":"2020091709242425200_ref35","doi-asserted-by":"crossref","first-page":"80","DOI":"10.1016\/j.sysconle.2014.04.009","article-title":"Optimal iterative learning control design for multi-agent systems consensus tracking","volume":"69","author":"Yang","year":"2014","journal-title":"Syst. Control Lett."},{"key":"2020091709242425200_ref36","doi-asserted-by":"crossref","first-page":"2669","DOI":"10.1109\/TCSI.2012.2190663","article-title":"Necessary and sufficient consensus conditions of descriptor multi-agent systems","volume":"59","author":"Yang","year":"2012","journal-title":"IEEE Trans. Circuits Syst. I: Regul. Pap."},{"key":"2020091709242425200_ref37","doi-asserted-by":"crossref","first-page":"389","DOI":"10.1049\/iet-cta.2013.0019","article-title":"Consensus of descriptor multi-agent systems via dynamic compensators","volume":"8","author":"Yang","year":"2014","journal-title":"IET Control Theory Appl."},{"key":"2020091709242425200_ref38","doi-asserted-by":"crossref","first-page":"2869","DOI":"10.1080\/00207721.2015.1034303","article-title":"Admissible consensus for heterogeneous descriptor multi-agent systems","volume":"47","author":"Yang","year":"2014","journal-title":"Int. J. Syst. Sci."},{"key":"2020091709242425200_ref39","doi-asserted-by":"crossref","first-page":"651","DOI":"10.1016\/j.neucom.2017.05.073","article-title":"Leader-following guaranteed-performance consensus design for singular multi-agent systems with Lipschitz nonlinear dynamics","volume":"266","author":"Zheng","year":"2017","journal-title":"Neurocomputing"},{"key":"2020091709242425200_ref40","doi-asserted-by":"crossref","first-page":"1359","DOI":"10.1109\/TNNLS.2017.2651402","article-title":"Consensus of hybrid multi-agent systems","volume":"29","author":"Zheng","year":"2018","journal-title":"IEEE Trans. Neural Netw. Learn. Syst."}],"container-title":["IMA Journal of Mathematical Control and Information"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/academic.oup.com\/imamci\/article-pdf\/37\/2\/535\/33762504\/dnz012.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"syndication"},{"URL":"http:\/\/academic.oup.com\/imamci\/article-pdf\/37\/2\/535\/33762504\/dnz012.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,7,17]],"date-time":"2024-07-17T04:50:40Z","timestamp":1721191840000},"score":1,"resource":{"primary":{"URL":"https:\/\/academic.oup.com\/imamci\/article\/37\/2\/535\/5466098"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,4,23]]},"references-count":40,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2019,4,23]]},"published-print":{"date-parts":[[2020,6,6]]}},"URL":"https:\/\/doi.org\/10.1093\/imamci\/dnz012","relation":{},"ISSN":["0265-0754","1471-6887"],"issn-type":[{"value":"0265-0754","type":"print"},{"value":"1471-6887","type":"electronic"}],"subject":[],"published-other":{"date-parts":[[2020,6]]},"published":{"date-parts":[[2019,4,23]]}}}