{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,15]],"date-time":"2026-10-15T03:42:18Z","timestamp":1792035738411,"version":"4.4.0"},"reference-count":44,"publisher":"MDPI AG","issue":"17","license":[{"start":{"date-parts":[[2025,9,8]],"date-time":"2025-09-08T00:00:00Z","timestamp":1757289600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100012166","name":"the National Key Research and Development Program of China","doi-asserted-by":"publisher","award":["2021YFC2202600"],"award-info":[{"award-number":["2021YFC2202600"]}],"id":[{"id":"10.13039\/501100012166","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>The issue of in-orbit optimal safe surrounding control for service satellite (SSat) formation against a huge unknown target satellite (TSat) with specific structures is solved by using relative measurements only, and an optimal cooperative safe surrounding (OCSS) hybrid controller achieving both target tracking (TT) and configuration tracking (CT) is proposed corresponding to the two equal sub-objectives. Facing the challenges caused by incomplete information of the TSat, by using relative measurements only, the initial-condition-free boundaries are constructed by an arctan-based state transformation to directly constrain the target tracking error to perform prescribed transient and steady-state behaviors. Based on the shared TT control law, optimal collision-free CT controllers for all SSats are further solved via a nonzero-sum differential game, where the collision threat from all SSats and target structures are modeled by a novel circumscribed-sphere model. Finally, the effectiveness and advantages of the proposed OCSS control technique is verified by simulation results.<\/jats:p>","DOI":"10.3390\/s25175606","type":"journal-article","created":{"date-parts":[[2025,9,9]],"date-time":"2025-09-09T19:16:17Z","timestamp":1757445377000},"page":"5606","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["In-Orbit Optimal Safe Formation Control for Surrounding an Unknown Huge Target with Specific Structure by Using Relative Sensors Only"],"prefix":"10.3390","volume":"25","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-7651-7143","authenticated-orcid":false,"given":"Bosong","family":"Wei","sequence":"first","affiliation":[{"name":"School of Astronautics, Northwestern Polytechnical University, 127 Youyi West Road, Xi\u2019an 710072, China"},{"name":"National Key Laboratory of Aerospace Flight Dynamics, Northwestern Polytechnical University, Xi\u2019an 710072, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Cong","family":"Li","sequence":"additional","affiliation":[{"name":"School of Astronautics, Northwestern Polytechnical University, 127 Youyi West Road, Xi\u2019an 710072, China"},{"name":"National Key Laboratory of Aerospace Flight Dynamics, Northwestern Polytechnical University, Xi\u2019an 710072, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7960-5704","authenticated-orcid":false,"given":"Zhaohui","family":"Dang","sequence":"additional","affiliation":[{"name":"School of Astronautics, Northwestern Polytechnical University, 127 Youyi West Road, Xi\u2019an 710072, China"},{"name":"National Key Laboratory of Aerospace Flight Dynamics, Northwestern Polytechnical University, Xi\u2019an 710072, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Xiaokui","family":"Yue","sequence":"additional","affiliation":[{"name":"School of Astronautics, Northwestern Polytechnical University, 127 Youyi West Road, Xi\u2019an 710072, China"},{"name":"National Key Laboratory of Aerospace Flight Dynamics, Northwestern Polytechnical University, Xi\u2019an 710072, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2025,9,8]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"110746","DOI":"10.1016\/j.automatica.2022.110746","article-title":"Dynamic Generalized Nash Equilibrium Seeking for N-Coalition Noncooperative Games","volume":"147","author":"Liu","year":"2023","journal-title":"Automatica"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"2392","DOI":"10.1109\/TNSE.2022.3163447","article-title":"Distributed Nash Equilibrium Seeking of N-Coalition Noncooperative Games with Application to UAV Swarms","volume":"9","author":"Liu","year":"2022","journal-title":"IEEE Trans. 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