{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,12]],"date-time":"2026-05-12T21:22:07Z","timestamp":1778620927120,"version":"3.51.4"},"reference-count":36,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2022,2,21]],"date-time":"2022-02-21T00:00:00Z","timestamp":1645401600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100004826","name":"Beijing Natural Science Foundation","doi-asserted-by":"publisher","award":["L202016"],"award-info":[{"award-number":["L202016"]}],"id":[{"id":"10.13039\/501100004826","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["61901011"],"award-info":[{"award-number":["61901011"]}],"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":["62001011"],"award-info":[{"award-number":["62001011"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Scientific Research Plan of Beijing Municipal Commission of Education","award":["KM201910005026"],"award-info":[{"award-number":["KM201910005026"]}]},{"name":"Beijing Nova Program of Science and Technology","award":["Z191100001119094"],"award-info":[{"award-number":["Z191100001119094"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>With the rapid development of UAV technology, the research of optimal UAV formation tracking has been extensively studied. However, the high maneuverability and dynamic network topology of UAVs make formation tracking control much more difficult. In this paper, considering the highly dynamic features of uncertain time-varying leader velocity and network-induced delays, the optimal formation control algorithms for both near-equilibrium and general dynamic control cases are developed. First, the discrete-time error dynamics of UAV leader\u2013follower models are analyzed. Next, a linear quadratic optimization problem is formulated with the objective of minimizing the errors between the desired and actual states consisting of velocity and position information of the follower. The optimal formation tracking problem of near-equilibrium cases is addressed by using a backward recursion method, and then the results are further extended to the general dynamic case where the leader moves at an uncertain time-varying velocity. Additionally, angle deviations are investigated, and it is proved that the similar state dynamics to the general case can be derived and the principle of control strategy design can be maintained. By using actual real-world data, numerical experiments verify the effectiveness of the proposed optimal UAV formation-tracking algorithm in both near-equilibrium and dynamic control cases in the presence of network-induced delays.<\/jats:p>","DOI":"10.3390\/e24020305","type":"journal-article","created":{"date-parts":[[2022,2,21]],"date-time":"2022-02-21T20:24:21Z","timestamp":1645475061000},"page":"305","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":8,"title":["Optimal UAV Formation Tracking Control with Dynamic Leading Velocity and Network-Induced Delays"],"prefix":"10.3390","volume":"24","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-2880-3329","authenticated-orcid":false,"given":"Zhuwei","family":"Wang","sequence":"first","affiliation":[{"name":"Faculty of Information Technology, Beijing University of Technology, Beijing 100124, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Mengjiao","family":"Xu","sequence":"additional","affiliation":[{"name":"Faculty of Information Technology, Beijing University of Technology, Beijing 100124, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Lihan","family":"Liu","sequence":"additional","affiliation":[{"name":"School of Information, Beijing Wuzi University, Beijing 101149, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Chao","family":"Fang","sequence":"additional","affiliation":[{"name":"Faculty of Information Technology, Beijing University of Technology, Beijing 100124, China"},{"name":"Purple Mountain Laboratory: Networking, Communications and Security, Nanjing 210096, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8470-3982","authenticated-orcid":false,"given":"Yang","family":"Sun","sequence":"additional","affiliation":[{"name":"Faculty of Information Technology, Beijing University of Technology, Beijing 100124, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2799-6464","authenticated-orcid":false,"given":"Huamin","family":"Chen","sequence":"additional","affiliation":[{"name":"Faculty of Information Technology, Beijing University of Technology, Beijing 100124, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2022,2,21]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1123","DOI":"10.1109\/COMST.2015.2495297","article-title":"Survey of important issues in UAV communication networks","volume":"18","author":"Gupta","year":"2015","journal-title":"IEEE Commun. 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