{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T01:43:03Z","timestamp":1760060583082,"version":"build-2065373602"},"reference-count":47,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2025,9,2]],"date-time":"2025-09-02T00:00:00Z","timestamp":1756771200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100018542","name":"Natural Science Foundation of Sichuan Province","doi-asserted-by":"publisher","award":["2024NSFSC0021","MZGC20240139","ZYGX2024K028","ZYGX2025K028"],"award-info":[{"award-number":["2024NSFSC0021","MZGC20240139","ZYGX2024K028","ZYGX2025K028"]}],"id":[{"id":"10.13039\/501100018542","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Sichuan Science and Technology Programs","award":["2024NSFSC0021","MZGC20240139","ZYGX2024K028","ZYGX2025K028"],"award-info":[{"award-number":["2024NSFSC0021","MZGC20240139","ZYGX2024K028","ZYGX2025K028"]}]},{"name":"Fundamental Research Funds for the Central Universities","award":["2024NSFSC0021","MZGC20240139","ZYGX2024K028","ZYGX2025K028"],"award-info":[{"award-number":["2024NSFSC0021","MZGC20240139","ZYGX2024K028","ZYGX2025K028"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>Signed networks, which incorporate both cooperative and antagonistic interactions, naturally give rise to symmetric behaviors in multi-agent systems. One such behavior is bipartite containment tracking, where follower agents converge to a symmetric configuration determined by multiple groups of leaders with opposing influence. Moreover, a timely response is critical to ensuring high performance in containment tracking tasks, particularly for high-order multi-agent systems operating in dynamic and uncertain environments. To this end, this paper investigates the predefined-time bipartite containment tracking problem for high-order multi-agent systems affected by external disturbances. A robust tracking control scheme is developed based on the backstepping method to ensure that the tracking errors converge to a predefined residual set within a user-specified time. The convergence time is explicitly adjustable through a design parameter, and the proposed scheme effectively avoids the singularities often encountered in conventional predefined-time control approaches. The stability and robustness of the proposed scheme are rigorously established through Lyapunov-based analysis, and extensive simulation results are provided to validate our theoretical findings.<\/jats:p>","DOI":"10.3390\/sym17091425","type":"journal-article","created":{"date-parts":[[2025,9,2]],"date-time":"2025-09-02T08:23:38Z","timestamp":1756801418000},"page":"1425","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Symmetric Bipartite Containment Tracking of High-Order Networked Agents via Predefined-Time Backstepping Control"],"prefix":"10.3390","volume":"17","author":[{"given":"Bowen","family":"Chen","sequence":"first","affiliation":[{"name":"School of Aeronautics and Astronautics, University of Electronic Science and Technology of China, Chengdu 611731, China"},{"name":"Aircraft Swarm Intelligent Sensing and Cooperative Control Key Laboratory of Sichuan Province, Chengdu 611731, China"}]},{"given":"Kaiyu","family":"Qin","sequence":"additional","affiliation":[{"name":"School of Aeronautics and Astronautics, University of Electronic Science and Technology of China, Chengdu 611731, China"},{"name":"Aircraft Swarm Intelligent Sensing and Cooperative Control Key Laboratory of Sichuan Province, Chengdu 611731, China"},{"name":"National Laboratory on Adaptive Optics, Chengdu 610209, China"}]},{"ORCID":"https:\/\/orcid.org\/0009-0001-0877-2000","authenticated-orcid":false,"given":"Zhiqiang","family":"Li","sequence":"additional","affiliation":[{"name":"School of Aeronautics and Astronautics, University of Electronic Science and Technology of China, Chengdu 611731, China"},{"name":"Aircraft Swarm Intelligent Sensing and Cooperative Control Key Laboratory of Sichuan Province, Chengdu 611731, China"},{"name":"National Laboratory on Adaptive Optics, Chengdu 610209, China"}]},{"given":"Mengji","family":"Shi","sequence":"additional","affiliation":[{"name":"School of Aeronautics and Astronautics, University of Electronic Science and Technology of China, Chengdu 611731, China"},{"name":"Aircraft Swarm Intelligent Sensing and Cooperative Control Key Laboratory of Sichuan Province, Chengdu 611731, China"},{"name":"National Laboratory on Adaptive Optics, Chengdu 610209, China"}]}],"member":"1968","published-online":{"date-parts":[[2025,9,2]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Li, W., Yan, S., Shi, L., Yue, J., Shi, M., Lin, B., and Qin, K. 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