{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,29]],"date-time":"2026-05-29T11:24:09Z","timestamp":1780053849496,"version":"3.54.0"},"reference-count":28,"publisher":"MDPI AG","issue":"5","license":[{"start":{"date-parts":[[2025,5,17]],"date-time":"2025-05-17T00:00:00Z","timestamp":1747440000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["62473278"],"award-info":[{"award-number":["62473278"]}],"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":["145409322"],"award-info":[{"award-number":["145409322"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Basic Scientific Research Funds Project for Provincial Colleges and Universities of Heilongjiang Province","award":["62473278"],"award-info":[{"award-number":["62473278"]}]},{"name":"Basic Scientific Research Funds Project for Provincial Colleges and Universities of Heilongjiang Province","award":["145409322"],"award-info":[{"award-number":["145409322"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>This paper proposes a fixed-time formation-tracking control problem for a heterogeneous multi-agent system (MAS) consisting of six unmanned aerial vehicles (UAVs) and three unmanned ground vehicles (UGVs) under actuator attacks, external disturbances, and input saturation. First, a distributed sliding mode estimator and controller tailored for UAV-UGV heterogeneous systems are proposed based on sliding mode techniques. Second, by integrating repulsive potential functions with sliding manifolds, a distributed fixed-time adaptive sliding mode control protocol was designed. This protocol ensures collision avoidance while enabling the MASs to track desired trajectories and achieve a predefined formation configuration within a fixed time. The fixed-time stability of the closed-loop system was rigorously proven via Lyapunov theory.<\/jats:p>","DOI":"10.3390\/e27050538","type":"journal-article","created":{"date-parts":[[2025,5,19]],"date-time":"2025-05-19T07:34:03Z","timestamp":1747640043000},"page":"538","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Fixed-Time Cooperative Formation Control of Heterogeneous Systems Under Multiple Constraints"],"prefix":"10.3390","volume":"27","author":[{"ORCID":"https:\/\/orcid.org\/0009-0009-2907-3645","authenticated-orcid":false,"given":"Yandong","family":"Li","sequence":"first","affiliation":[{"name":"College of Computer and Control Engineering, Qiqihar University, Qiqihar 161000, China"},{"name":"Heilongjiang Key Laboratory of Big Data Network Security Detection and Analysis, Qiqihar University, Qiqihar 161000, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0009-0002-2348-6907","authenticated-orcid":false,"given":"Wei","family":"Zhao","sequence":"additional","affiliation":[{"name":"College of Computer and Control Engineering, Qiqihar University, Qiqihar 161000, China"},{"name":"Heilongjiang Key Laboratory of Big Data Network Security Detection and Analysis, Qiqihar University, Qiqihar 161000, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0009-0005-0459-1308","authenticated-orcid":false,"given":"Ling","family":"Zhu","sequence":"additional","affiliation":[{"name":"School of Mechanical and Electrical Engineering, Qiqihar University, Qiqihar 161000, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Zehua","family":"Zhang","sequence":"additional","affiliation":[{"name":"College of Computer and Control Engineering, Qiqihar University, Qiqihar 161000, China"},{"name":"Heilongjiang Key Laboratory of Big Data Network Security Detection and Analysis, Qiqihar University, Qiqihar 161000, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yuan","family":"Guo","sequence":"additional","affiliation":[{"name":"School of Computer and Big Data, Heilongjiang University, Harbin 150080, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2025,5,17]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1450","DOI":"10.1002\/rob.21723","article-title":"Radiation search operations using scene understanding with autonomous UAV and UGV","volume":"34","author":"Christie","year":"2017","journal-title":"J. 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