{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,4]],"date-time":"2026-05-04T16:08:32Z","timestamp":1777910912104,"version":"3.51.4"},"reference-count":34,"publisher":"SAGE Publications","issue":"13","license":[{"start":{"date-parts":[[2024,3,10]],"date-time":"2024-03-10T00:00:00Z","timestamp":1710028800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/journals.sagepub.com\/page\/policies\/text-and-data-mining-license"}],"funder":[{"DOI":"10.13039\/501100012226","name":"the Fundamental Research Funds for the Central Universities","doi-asserted-by":"publisher","award":["Grant No. FRF-TP-18-012A3"],"award-info":[{"award-number":["Grant No. FRF-TP-18-012A3"]}],"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":["Grant No. 61304170"],"award-info":[{"award-number":["Grant No. 61304170"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["journals.sagepub.com"],"crossmark-restriction":true},"short-container-title":["Transactions of the Institute of Measurement and Control"],"published-print":{"date-parts":[[2024,9]]},"abstract":"<jats:p>This paper studies the exponential finite-time formation problems for a group of locomotive agents that maintain order on a circle. In an ideal environment, that is, without external disturbances, a combined protocol with linear continuous-time states and their nonlinear continuous functions is proposed. Each agent can adjust the movement speed itself by changing the exponent of the nonlinear function. The obtained closed-loop system will converge with an exponential speed when the initial states of the agents are far from the target location, and with a finite-time speed nearby. For the case with external disturbances, a combined protocol with linear continuous-time states and their sign functions is presented. Due to the discontinuity of the sign functions, the Filippov solutions are employed. The exponential finite-time circle formation will be achieved even in the existence of external disturbances. Moreover, the above result is extended to the application in circle containment, where the defenders will form a circle formation to surround the swarm of protectees. Finally, several computational simulations illustrate the validity of the proposed protocols.<\/jats:p>","DOI":"10.1177\/01423312241232354","type":"journal-article","created":{"date-parts":[[2024,3,11]],"date-time":"2024-03-11T02:10:48Z","timestamp":1710123048000},"page":"2477-2486","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":2,"title":["Exponential finite-time circle formation of multi-agent systems and its application in circle containment"],"prefix":"10.1177","volume":"46","author":[{"ORCID":"https:\/\/orcid.org\/0009-0005-4577-5285","authenticated-orcid":false,"given":"Xiaolin","family":"Zhu","sequence":"first","affiliation":[{"name":"School of Mathematics and Physics, University of Science and Technology Beijing, China"}]},{"given":"Huiyang","family":"Liu","sequence":"additional","affiliation":[{"name":"School of Mathematics and Physics, University of Science and Technology Beijing, China"}]}],"member":"179","published-online":{"date-parts":[[2024,3,10]]},"reference":[{"key":"bibr1-01423312241232354","doi-asserted-by":"publisher","DOI":"10.1109\/TAC.2011.2174676"},{"issue":"1","key":"bibr2-01423312241232354","first-page":"33","volume":"57","author":"Cao Y","year":"2011","journal-title":"IEEE Transactions on Automatic Control"},{"key":"bibr3-01423312241232354","doi-asserted-by":"publisher","DOI":"10.1177\/01423312221088087"},{"key":"bibr4-01423312241232354","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-540-24838-5_12"},{"key":"bibr5-01423312241232354","doi-asserted-by":"publisher","DOI":"10.1137\/1.9781611971309"},{"key":"bibr6-01423312241232354","doi-asserted-by":"publisher","DOI":"10.1145\/584490.584509"},{"key":"bibr7-01423312241232354","doi-asserted-by":"publisher","DOI":"10.1016\/j.tcs.2008.01.050"},{"key":"bibr8-01423312241232354","doi-asserted-by":"publisher","DOI":"10.1016\/j.automatica.2013.02.024"},{"key":"bibr9-01423312241232354","doi-asserted-by":"publisher","DOI":"10.1080\/00207179.2012.713515"},{"key":"bibr10-01423312241232354","volume-title":"Differential Equations with Discontinuous Righthand Sides: Control Systems","volume":"18","author":"Filippov AF","year":"2013"},{"key":"bibr11-01423312241232354","doi-asserted-by":"publisher","DOI":"10.1177\/0142331217693918"},{"key":"bibr12-01423312241232354","doi-asserted-by":"publisher","DOI":"10.1080\/00207170802123895"},{"key":"bibr13-01423312241232354","doi-asserted-by":"publisher","DOI":"10.1016\/j.automatica.2016.01.076"},{"key":"bibr14-01423312241232354","doi-asserted-by":"publisher","DOI":"10.1080\/00207179.2014.944872"},{"key":"bibr15-01423312241232354","doi-asserted-by":"publisher","DOI":"10.1109\/TSMC.2018.2816060"},{"key":"bibr16-01423312241232354","doi-asserted-by":"publisher","DOI":"10.1016\/j.automatica.2012.05.010"},{"issue":"8","key":"bibr17-01423312241232354","first-page":"3440","volume":"69","author":"Liu K","year":"2022","journal-title":"IEEE Transactions on Circuits and Systems II: Express Briefs"},{"key":"bibr18-01423312241232354","doi-asserted-by":"publisher","DOI":"10.1109\/TAC.2004.837589"},{"key":"bibr19-01423312241232354","doi-asserted-by":"publisher","DOI":"10.1109\/TAC.2015.2480336"},{"key":"bibr20-01423312241232354","doi-asserted-by":"publisher","DOI":"10.1109\/TAC.2005.864190"},{"key":"bibr21-01423312241232354","doi-asserted-by":"publisher","DOI":"10.1109\/TAC.2004.834113"},{"key":"bibr22-01423312241232354","doi-asserted-by":"publisher","DOI":"10.1109\/TCS.1987.1086038"},{"key":"bibr23-01423312241232354","doi-asserted-by":"publisher","DOI":"10.1016\/j.actaastro.2017.04.011"},{"key":"bibr24-01423312241232354","doi-asserted-by":"publisher","DOI":"10.1109\/ICIST.2019.8836812"},{"key":"bibr25-01423312241232354","doi-asserted-by":"publisher","DOI":"10.1137\/S009753979628292X"},{"key":"bibr26-01423312241232354","doi-asserted-by":"publisher","DOI":"10.1016\/j.automatica.2014.02.036"},{"key":"bibr27-01423312241232354","doi-asserted-by":"publisher","DOI":"10.1109\/CDC.2012.6426357"},{"key":"bibr28-01423312241232354","first-page":"7320","volume-title":"Proceedings of the 32nd Chinese control conference","author":"Wang C","year":"2013"},{"key":"bibr29-01423312241232354","doi-asserted-by":"publisher","DOI":"10.1109\/TAC.2010.2041610"},{"key":"bibr30-01423312241232354","doi-asserted-by":"publisher","DOI":"10.1016\/j.automatica.2009.07.012"},{"key":"bibr31-01423312241232354","doi-asserted-by":"publisher","DOI":"10.1109\/TAC.2021.3131549"},{"key":"bibr32-01423312241232354","doi-asserted-by":"publisher","DOI":"10.1177\/01423312211005277"},{"key":"bibr33-01423312241232354","doi-asserted-by":"publisher","DOI":"10.1109\/JAS.2023.123231"},{"key":"bibr34-01423312241232354","doi-asserted-by":"publisher","DOI":"10.1080\/00207179.2012.717722"}],"container-title":["Transactions of the Institute of Measurement and Control"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.1177\/01423312241232354","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/journals.sagepub.com\/doi\/full-xml\/10.1177\/01423312241232354","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.1177\/01423312241232354","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,5,1]],"date-time":"2026-05-01T15:09:52Z","timestamp":1777648192000},"score":1,"resource":{"primary":{"URL":"https:\/\/journals.sagepub.com\/doi\/10.1177\/01423312241232354"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,3,10]]},"references-count":34,"journal-issue":{"issue":"13","published-print":{"date-parts":[[2024,9]]}},"alternative-id":["10.1177\/01423312241232354"],"URL":"https:\/\/doi.org\/10.1177\/01423312241232354","relation":{},"ISSN":["0142-3312","1477-0369"],"issn-type":[{"value":"0142-3312","type":"print"},{"value":"1477-0369","type":"electronic"}],"subject":[],"published":{"date-parts":[[2024,3,10]]}}}