{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T15:04:21Z","timestamp":1753887861285,"version":"3.41.2"},"reference-count":30,"publisher":"Wiley","issue":"1","license":[{"start":{"date-parts":[[2021,8,31]],"date-time":"2021-08-31T00:00:00Z","timestamp":1630368000000},"content-version":"vor","delay-in-days":242,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100002842","name":"Chiang Mai University","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100002842","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["Complexity"],"published-print":{"date-parts":[[2021,1]]},"abstract":"<jats:p>The Cucker and Smale model is a well\u2010known flocking model that describes the emergence of flocks based on alignment. The first part focuses on investigating this model, including the effect of time delay and the presence of a leader. Furthermore, the control function is inserted into the dynamics of a leader to drive a group of agents to target. In the second part of this work, leadership\u2010based optimal control is investigated. Moreover, the existence of the first\u2010order optimality conditions for a delayed optimal control problem is discussed. Furthermore, the Runge\u2013Kutta discretization method and the nonlinear conjugate gradient method are employed to solve the discrete optimality system. Finally, the capacity of the proposed control approach to drive a group of agents to reach the desired places or track the trajectory is demonstrated by numerical experiment results.<\/jats:p>","DOI":"10.1155\/2021\/5545551","type":"journal-article","created":{"date-parts":[[2021,8,31]],"date-time":"2021-08-31T17:56:07Z","timestamp":1630432567000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Optimal Control through Leadership of the Cucker and Smale Flocking Model with Time Delays"],"prefix":"10.1155","volume":"2021","author":[{"given":"Adsadang","family":"Himakalasa","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3923-0415","authenticated-orcid":false,"given":"Suttida","family":"Wongkaew","sequence":"additional","affiliation":[]}],"member":"311","published-online":{"date-parts":[[2021,8,31]]},"reference":[{"key":"e_1_2_9_1_2","doi-asserted-by":"publisher","DOI":"10.1073\/pnas.0711437105"},{"key":"e_1_2_9_2_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.matcom.2008.11.018"},{"key":"e_1_2_9_3_2","doi-asserted-by":"publisher","DOI":"10.1137\/090746677"},{"key":"e_1_2_9_4_2","doi-asserted-by":"publisher","DOI":"10.1007\/978-0-8176-4946-3_13"},{"key":"e_1_2_9_5_2","doi-asserted-by":"publisher","DOI":"10.1109\/tac.2007.895842"},{"key":"e_1_2_9_6_2","doi-asserted-by":"publisher","DOI":"10.1098\/rspa.2009.0239"},{"key":"e_1_2_9_7_2","doi-asserted-by":"crossref","unstructured":"ChuangY.-L. 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