{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,26]],"date-time":"2025-09-26T00:18:22Z","timestamp":1758845902085,"version":"3.44.0"},"reference-count":39,"publisher":"Springer Science and Business Media LLC","issue":"10","license":[{"start":{"date-parts":[[2025,8,29]],"date-time":"2025-08-29T00:00:00Z","timestamp":1756425600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by-nc-nd\/4.0"},{"start":{"date-parts":[[2025,8,29]],"date-time":"2025-08-29T00:00:00Z","timestamp":1756425600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by-nc-nd\/4.0"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["62073216"],"award-info":[{"award-number":["62073216"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Complex Intell. Syst."],"published-print":{"date-parts":[[2025,10]]},"DOI":"10.1007\/s40747-025-02063-9","type":"journal-article","created":{"date-parts":[[2025,8,29]],"date-time":"2025-08-29T06:07:35Z","timestamp":1756447655000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Alternating direction response dynamics for distributed multi-agent interaction and formation coordination"],"prefix":"10.1007","volume":"11","author":[{"given":"Zhaohui","family":"Yang","sequence":"first","affiliation":[]},{"given":"Yuhao","family":"Jing","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8887-5845","authenticated-orcid":false,"given":"Pingfang","family":"Zhou","sequence":"additional","affiliation":[]},{"given":"Yupeng","family":"Zhang","sequence":"additional","affiliation":[]},{"given":"Lili","family":"Zhang","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2025,8,29]]},"reference":[{"issue":"5","key":"2063_CR1","doi-asserted-by":"publisher","first-page":"3897","DOI":"10.1007\/s10462-021-10097-x","volume":"55","author":"A Amirkhani","year":"2022","unstructured":"Amirkhani A, Barshooi AH (2022) Consensus in multi-agent systems: a review. Artif Intell Rev 55(5):3897\u20133935","journal-title":"Artif Intell Rev"},{"issue":"12","key":"2063_CR2","doi-asserted-by":"publisher","first-page":"19,319","DOI":"10.1109\/TITS.2024.3465046","volume":"25","author":"D Chu","year":"2024","unstructured":"Chu D, Zhao C, Wang R et al (2024) A survey of multi-vehicle consensus in uncertain networks for autonomous driving. IEEE Trans Intell Transp Syst 25(12):19,319-19,341","journal-title":"IEEE Trans Intell Transp Syst"},{"key":"2063_CR3","unstructured":"Farges JL, Perotto FS, Pralet C et\u00a0al (2024) Going beyond mono-mission earth observation: Using the multi-agent paradigm to federate multiple missions. In: 23rd International Conference on Autonomous Agents and Multiagent Systems (AAMAS-24), International Foundation for Autonomous Agents and Multiagent Systems, pp 2674\u20132678"},{"issue":"5","key":"2063_CR4","doi-asserted-by":"publisher","first-page":"4651","DOI":"10.1109\/TNSE.2024.3432746","volume":"11","author":"Y Zhou","year":"2024","unstructured":"Zhou Y, Jin Z, Shi H et al (2024) Enhanced emergency communication services for post\u2013disaster rescue: multi-irs assisted air-ground integrated data collection. IEEE Trans Netw Sci Eng 11(5):4651\u20134664","journal-title":"IEEE Trans Netw Sci Eng"},{"key":"2063_CR5","doi-asserted-by":"publisher","DOI":"10.1007\/978-4-431-55645-9","volume-title":"Non-cooperative game theory","author":"T Fujiwara-Greve","year":"2015","unstructured":"Fujiwara-Greve T (2015) Non-cooperative game theory. Springer, Berlin"},{"issue":"5","key":"2063_CR6","doi-asserted-by":"publisher","first-page":"763","DOI":"10.1109\/JAS.2022.105506","volume":"9","author":"Y Hong","year":"2022","unstructured":"Hong Y, Wang J, Wang J et al (2022) Cooperative and competitive multi-agent systems: from optimization to games. IEEE\/CAA J Autom Sin 9(5):763\u2013783","journal-title":"IEEE\/CAA J Autom Sin"},{"issue":"2","key":"2063_CR7","doi-asserted-by":"publisher","first-page":"140","DOI":"10.1109\/JPROC.2023.3234687","volume":"111","author":"M Ye","year":"2023","unstructured":"Ye M, Han QL, Ding L et al (2023) Distributed nash equilibrium seeking in games with partial decision information: A survey. Proc IEEE 111(2):140\u2013157","journal-title":"Proc IEEE"},{"key":"2063_CR8","doi-asserted-by":"crossref","unstructured":"Hu H, Dragotto G, Zhang Z et\u00a0al (2024) Who plays first? optimizing the order of play in stackelberg games with many robots. arXiv:2402.09246","DOI":"10.15607\/RSS.2024.XX.116"},{"key":"2063_CR9","unstructured":"Zhu EL (2024) From cooperation to competition: Prediction and planning in constrained multi-agent settings using data-driven and model-based optimal control methods. PhD thesis, University of California, Berkeley"},{"key":"2063_CR10","doi-asserted-by":"crossref","unstructured":"Fridovich-Keil D, Ratner E, Peters L et\u00a0al (2020) Efficient iterative linear-quadratic approximations for nonlinear multi-player general-sum differential games. In: 2020 IEEE international conference on robotics and automation (ICRA), IEEE, pp 1475\u20131481","DOI":"10.1109\/ICRA40945.2020.9197129"},{"issue":"1","key":"2063_CR11","doi-asserted-by":"publisher","first-page":"201","DOI":"10.1007\/s10514-021-10024-7","volume":"46","author":"S Le Cleac\u2019h","year":"2022","unstructured":"Le Cleac\u2019h S, Schwager M, Manchester Z (2022) Algames: a fast augmented lagrangian solver for constrained dynamic games. Auton Robot 46(1):201\u2013215","journal-title":"Auton Robot"},{"key":"2063_CR12","doi-asserted-by":"crossref","unstructured":"Zhu EL, Borrelli F (2023) A sequential quadratic programming approach to the solution of open-loop generalized nash equilibria. In: 2023 IEEE International Conference on Robotics and Automation (ICRA), IEEE, pp 3211\u20133217","DOI":"10.1109\/ICRA48891.2023.10160799"},{"issue":"7","key":"2063_CR13","doi-asserted-by":"publisher","first-page":"4139","DOI":"10.1109\/LRA.2023.3280809","volume":"8","author":"X Liu","year":"2023","unstructured":"Liu X, Peters L, Alonso-Mora J (2023) Learning to play trajectory games against opponents with unknown objectives. IEEE Rob Autom Lett 8(7):4139\u20134146","journal-title":"IEEE Rob Autom Lett"},{"issue":"5","key":"2063_CR14","doi-asserted-by":"publisher","first-page":"1389","DOI":"10.1109\/TRO.2020.2994881","volume":"36","author":"R Spica","year":"2020","unstructured":"Spica R, Cristofalo E, Wang Z et al (2020) A real-time game theoretic planner for autonomous two-player drone racing. IEEE Trans Rob 36(5):1389\u20131403","journal-title":"IEEE Trans Rob"},{"issue":"4","key":"2063_CR15","doi-asserted-by":"publisher","first-page":"1313","DOI":"10.1109\/TRO.2020.3047521","volume":"37","author":"M Wang","year":"2021","unstructured":"Wang M, Wang Z, Talbot J et al (2021) Game-theoretic planning for self-driving cars in multivehicle competitive scenarios. IEEE Trans Rob 37(4):1313\u20131325","journal-title":"IEEE Trans Rob"},{"key":"2063_CR16","doi-asserted-by":"crossref","unstructured":"Zhao Y, Zhu Q (2023) Stackelberg meta-learning for strategic guidance in multi-robot trajectory planning. In: 2023 IEEE\/RSJ International Conference on Intelligent Robots and Systems (IROS), IEEE, pp 11,342\u201311,347","DOI":"10.1109\/IROS55552.2023.10342202"},{"key":"2063_CR17","doi-asserted-by":"publisher","first-page":"2487","DOI":"10.1109\/LCSYS.2024.3491052","volume":"8","author":"S Williams","year":"2024","unstructured":"Williams S, Deshmukh J (2024) Potential games on cubic splines for self-interested multi-agent motion planning. IEEE Control Syst Lett 8:2487\u20132492","journal-title":"IEEE Control Syst Lett"},{"issue":"6","key":"2063_CR18","doi-asserted-by":"publisher","first-page":"343","DOI":"10.1007\/s40314-024-02861-w","volume":"43","author":"B Varga","year":"2024","unstructured":"Varga B, Huang D, Hohmann S (2024) Identification methods for ordinal potential differential games. Comput Appl Math 43(6):343","journal-title":"Comput Appl Math"},{"issue":"8","key":"2063_CR19","doi-asserted-by":"publisher","first-page":"8014","DOI":"10.1109\/TITS.2023.3264665","volume":"24","author":"M Liu","year":"2023","unstructured":"Liu M, Kolmanovsky I, Tseng HE et al (2023) Potential game-based decision-making for autonomous driving. IEEE Trans Intell Transp Syst 24(8):8014\u20138027","journal-title":"IEEE Trans Intell Transp Syst"},{"key":"2063_CR20","doi-asserted-by":"crossref","unstructured":"Kavuncu T, Yaraneri A, Mehr N (2021) Potential ilqr: A potential-minimizing controller for planning multi-agent interactive trajectories. In: 17th Robotics: Science and Systems, RSS 2021, MIT Press Journals","DOI":"10.15607\/RSS.2021.XVII.084"},{"key":"2063_CR21","doi-asserted-by":"crossref","unstructured":"Williams Z, Chen J, Mehr N (2023) Distributed potential ilqr: Scalable game-theoretic trajectory planning for multi-agent interactions. In: 2023 IEEE International Conference on Robotics and Automation (ICRA), IEEE, pp 01\u201307","DOI":"10.1109\/ICRA48891.2023.10161176"},{"issue":"1","key":"2063_CR22","doi-asserted-by":"publisher","first-page":"637","DOI":"10.1109\/TAC.2023.3270367","volume":"69","author":"A Prasad","year":"2023","unstructured":"Prasad A, Mohapatra PS, Reddy PV (2023) On the structure of feedback potential difference games. IEEE Trans Autom Control 69(1):637\u2013644","journal-title":"IEEE Trans Autom Control"},{"issue":"11","key":"2063_CR23","doi-asserted-by":"publisher","first-page":"18,611","DOI":"10.1109\/TITS.2024.3436882","volume":"25","author":"Y Wang","year":"2024","unstructured":"Wang Y, Liu X, Wu Z et al (2024) Distributed prescribed-time formation control for underactuated surface vehicles with input saturation: theory and experiment. IEEE Trans Intell Transp Syst 25(11):18,611-18,623","journal-title":"IEEE Trans Intell Transp Syst"},{"issue":"12","key":"2063_CR24","doi-asserted-by":"publisher","first-page":"14,749","DOI":"10.1109\/TVT.2020.3039220","volume":"69","author":"W Zhou","year":"2020","unstructured":"Zhou W, Wang Y, Ahn CK et al (2020) Adaptive fuzzy backstepping-based formation control of unmanned surface vehicles with unknown model nonlinearity and actuator saturation. IEEE Trans Veh Technol 69(12):14,749-14,764","journal-title":"IEEE Trans Veh Technol"},{"issue":"05","key":"2063_CR25","doi-asserted-by":"publisher","first-page":"913","DOI":"10.1142\/S2301385024500274","volume":"12","author":"Y Liu","year":"2024","unstructured":"Liu Y, Liu J, He Z et al (2024) A survey of multi-agent systems on distributed formation control. Unmann Syst 12(05):913\u2013926","journal-title":"Unmann Syst"},{"issue":"1","key":"2063_CR26","doi-asserted-by":"publisher","first-page":"450","DOI":"10.1109\/TCNS.2020.3029155","volume":"8","author":"F Chen","year":"2020","unstructured":"Chen F, Dimarogonas DV (2020) Leader-follower formation control with prescribed performance guarantees. IEEE Trans Control Netw Syst 8(1):450\u2013461","journal-title":"IEEE Trans Control Netw Syst"},{"issue":"6","key":"2063_CR27","first-page":"3505","volume":"10","author":"H Yang","year":"2023","unstructured":"Yang H, Zhang H, Wang Z et al (2023) Reliable leader-following consensus of discrete-time semi-markovian jump multi-agent systems. IEEE Trans Netw Sci Eng 10(6):3505\u20133518","journal-title":"IEEE Trans Netw Sci Eng"},{"key":"2063_CR28","doi-asserted-by":"crossref","unstructured":"Ze K, Wang W, Liu K et al (2024) Time-varying formation planning and distributed control for multiple uavs in clutter environment. IEEE Trans Industr Electron 71(9):11,305-11,315","DOI":"10.1109\/TIE.2023.3335448"},{"issue":"3","key":"2063_CR29","doi-asserted-by":"publisher","first-page":"4419","DOI":"10.1109\/JSYST.2023.3268160","volume":"17","author":"Z Deng","year":"2023","unstructured":"Deng Z, Luo J, Liu Y et al (2023) Distributed formation control algorithms for quavs based on aggregative games. IEEE Syst J 17(3):4419\u20134429","journal-title":"IEEE Syst J"},{"issue":"3","key":"2063_CR30","doi-asserted-by":"publisher","first-page":"4972","DOI":"10.1109\/TII.2023.3331162","volume":"20","author":"Z Chen","year":"2024","unstructured":"Chen Z, Nian X, Meng Q (2024) Noncooperative formation control in the presence of malicious agents: A game-based strategy. IEEE Trans Industr Inf 20(3):4972\u20134981","journal-title":"IEEE Trans Industr Inf"},{"issue":"105","key":"2063_CR31","first-page":"743","volume":"142","author":"J Shi","year":"2024","unstructured":"Shi J, Ye M, Ding L et al (2024) Distributed least-distance formation control for euler-lagrange systems: A game-based approach. Control Eng Pract 142(105):743","journal-title":"Control Eng Pract"},{"issue":"1","key":"2063_CR32","doi-asserted-by":"publisher","first-page":"157","DOI":"10.1287\/moor.2018.0986","volume":"45","author":"J Lei","year":"2020","unstructured":"Lei J, Shanbhag UV, Pang JS et al (2020) On synchronous, asynchronous, and randomized best-response schemes for stochastic nash games. Math Oper Res 45(1):157\u2013190","journal-title":"Math Oper Res"},{"key":"2063_CR33","doi-asserted-by":"publisher","first-page":"254","DOI":"10.1007\/s13235-017-0218-6","volume":"8","author":"A Fonseca-Morales","year":"2018","unstructured":"Fonseca-Morales A, Hern\u00e1ndez-Lerma O (2018) Potential differential games. Dyn Games Appl 8:254\u2013279","journal-title":"Dyn Games Appl"},{"key":"2063_CR34","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-319-30869-2","volume-title":"Potential game theory","author":"QD L\u00e3","year":"2016","unstructured":"L\u00e3 QD, Chew YH, Soong BH (2016) Potential game theory. Springer International Publishing, Cham"},{"issue":"11","key":"2063_CR35","doi-asserted-by":"publisher","first-page":"12,754","DOI":"10.1109\/TITS.2023.3286898","volume":"24","author":"Z Huang","year":"2023","unstructured":"Huang Z, Shen S, Ma J (2023) Decentralized ilqr for cooperative trajectory planning of connected autonomous vehicles via dual consensus admm. IEEE Trans Intell Transp Syst 24(11):12,754-12,766","journal-title":"IEEE Trans Intell Transp Syst"},{"key":"2063_CR36","doi-asserted-by":"crossref","unstructured":"Howell TA, Jackson BE, Manchester Z (2019) Altro: A fast solver for constrained trajectory optimization. In: 2019 IEEE\/RSJ International Conference on Intelligent Robots and Systems (IROS), IEEE, pp 7674\u20137679","DOI":"10.1109\/IROS40897.2019.8967788"},{"key":"2063_CR37","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/s12532-018-0139-4","volume":"11","author":"JA Andersson","year":"2019","unstructured":"Andersson JA, Gillis J, Horn G et al (2019) Casadi: a software framework for nonlinear optimization and optimal control. Math Progr Comput 11:1\u201336","journal-title":"Math Progr Comput"},{"issue":"5","key":"2063_CR38","doi-asserted-by":"publisher","first-page":"2887","DOI":"10.1109\/TSMC.2022.3220837","volume":"53","author":"X Xu","year":"2022","unstructured":"Xu X, Gong Z, Herrera-Viedma E et al (2022) Consensus reaching in group decision making with linear uncertain preferences and asymmetric costs. IEEE Trans Syst Man Cybern Syst 53(5):2887\u20132899","journal-title":"IEEE Trans Syst Man Cybern Syst"},{"key":"2063_CR39","doi-asserted-by":"crossref","unstructured":"Sawamura R, Hayashi N, Inuiguchi M (2024) A distributed primal-dual push-sum algorithm on open multiagent networks. IEEE Trans Autom Control","DOI":"10.1109\/TAC.2024.3453382"}],"container-title":["Complex & Intelligent Systems"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s40747-025-02063-9.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s40747-025-02063-9\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s40747-025-02063-9.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,9,25]],"date-time":"2025-09-25T13:32:37Z","timestamp":1758807157000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s40747-025-02063-9"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,8,29]]},"references-count":39,"journal-issue":{"issue":"10","published-print":{"date-parts":[[2025,10]]}},"alternative-id":["2063"],"URL":"https:\/\/doi.org\/10.1007\/s40747-025-02063-9","relation":{},"ISSN":["2199-4536","2198-6053"],"issn-type":[{"type":"print","value":"2199-4536"},{"type":"electronic","value":"2198-6053"}],"subject":[],"published":{"date-parts":[[2025,8,29]]},"assertion":[{"value":"18 February 2025","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"13 August 2025","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"29 August 2025","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}},{"value":"Not applicable. The work presented in this research did not involve human participants or animal subjects, and therefore, did not require ethical approval concerning human or animal research.","order":3,"name":"Ethics","group":{"name":"EthicsHeading","label":"Ethics Approval"}},{"value":"Not applicable.","order":4,"name":"Ethics","group":{"name":"EthicsHeading","label":"Consent"}}],"article-number":"429"}}