{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,21]],"date-time":"2026-02-21T20:26:31Z","timestamp":1771705591534,"version":"3.50.1"},"reference-count":40,"publisher":"Springer Science and Business Media LLC","issue":"4","license":[{"start":{"date-parts":[[2024,4,17]],"date-time":"2024-04-17T00:00:00Z","timestamp":1713312000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2024,4,17]],"date-time":"2024-04-17T00:00:00Z","timestamp":1713312000000},"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":["62103341"],"award-info":[{"award-number":["62103341"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"National Key Research and Development Program of China","award":["2022YFE0133100"],"award-info":[{"award-number":["2022YFE0133100"]}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Complex Intell. Syst."],"published-print":{"date-parts":[[2024,8]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>This paper studies the problem of differentially private bipartite output consensus in continuous-time heterogeneous multi-agent systems (MASs) characterized by antagonistic interactions. A novel hybrid privacy-preserving event-triggered impulsive consensus protocol is introduced to protect the agent\u2019s initial information from disclosure, which involves a discrete-time information transmission based on an event-triggering mechanism. Using stochastic Lyapunov method, sufficient conditions have been obtained to achieve mean square bipartite output consensus with a guaranteed level of privacy. Furthermore, the differential privacy of competitive agent pairs is exclusively secured by the proposed control scheme by injecting Laplace noise. The protocol also effectively prevents Zeno behavior by imposing a lower bound for impulsive intervals under all event-triggered conditions. A simulation example is provided to validate the effectiveness of the theoretical result.<\/jats:p>","DOI":"10.1007\/s40747-024-01430-2","type":"journal-article","created":{"date-parts":[[2024,4,17]],"date-time":"2024-04-17T05:02:49Z","timestamp":1713330169000},"page":"5127-5137","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Privacy-preserving bipartite output consensus for continuous-time heterogeneous multi-agent systems via event-triggered impulsive control"],"prefix":"10.1007","volume":"10","author":[{"given":"Jiayue","family":"Ma","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7559-8604","authenticated-orcid":false,"given":"Jiangping","family":"Hu","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2024,4,17]]},"reference":[{"key":"1430_CR1","doi-asserted-by":"crossref","unstructured":"Montero EE, Mutahira H, Pico N, Muhammad MS (2024) Dynamic warning zone and a short-distance goal for autonomous robot navigation using deep reinforcement learning. Complex Intell Syst 10: 1149\u20131166","DOI":"10.1007\/s40747-023-01216-y"},{"key":"1430_CR2","doi-asserted-by":"publisher","first-page":"263","DOI":"10.1016\/j.ins.2022.11.035","volume":"619","author":"Q Wang","year":"2023","unstructured":"Wang Q, Hu J, Wu Y, Zhao Y (2023) Output synchronization of wide-area heterogeneous multi-agent systems over intermittent clustered networks. Inf Sci 619:263\u2013275","journal-title":"Inf Sci"},{"issue":"10","key":"1430_CR3","doi-asserted-by":"publisher","first-page":"6618","DOI":"10.1109\/TSMC.2022.3148295","volume":"52","author":"B Chen","year":"2022","unstructured":"Chen B, Hu J, Zhao Y, Ghosh BK (2022) Finite-time velocity-free rendezvous control of multiple AUV systems with intermittent communication. IEEE Trans Syst Man Cybern Syst 52(10):6618\u20136629","journal-title":"IEEE Trans Syst Man Cybern Syst"},{"issue":"5","key":"1430_CR4","doi-asserted-by":"publisher","first-page":"2122","DOI":"10.1109\/TAC.2018.2872197","volume":"64","author":"J Hu","year":"2018","unstructured":"Hu J, Wu Y, Li T, Ghosh BK (2018) Consensus control of general linear multiagent systems with antagonistic interactions and communication noises. IEEE Trans Autom Control 64(5):2122\u20132127","journal-title":"IEEE Trans Autom Control"},{"issue":"5","key":"1430_CR5","doi-asserted-by":"publisher","first-page":"3139","DOI":"10.1109\/TCYB.2022.3164048","volume":"53","author":"C Xu","year":"2023","unstructured":"Xu C, Xu H, Guan Z, Ge Y (2023) Observer-based dynamic event-triggered semiglobal bipartite consensus of linear multi-agent systems with input saturation. IEEE Trans Cybern 53(5):3139\u20133152","journal-title":"IEEE Trans Cybern"},{"key":"1430_CR6","doi-asserted-by":"publisher","first-page":"172","DOI":"10.1016\/j.automatica.2017.02.033","volume":"80","author":"FA Yaghmaie","year":"2017","unstructured":"Yaghmaie FA, Su R, Lewis FL, Olaru S (2017) Bipartite and cooperative output synchronizations of linear heterogeneous agents: a unified framework. Automatica 80:172\u2013176","journal-title":"Automatica"},{"issue":"11","key":"1430_CR7","doi-asserted-by":"publisher","first-page":"4816","DOI":"10.1109\/TNNLS.2019.2958107","volume":"31","author":"H Zhang","year":"2020","unstructured":"Zhang H, Cai Y, Wang Y, Su H (2020) Adaptive bipartite event-triggered output consensus of heterogeneous linear multiagent systems under fixed and switching topologies. IEEE Trans Neural Netw Learn Syst 31(11):4816\u20134830","journal-title":"IEEE Trans Neural Netw Learn Syst"},{"key":"1430_CR8","doi-asserted-by":"publisher","first-page":"1435","DOI":"10.1016\/j.ins.2022.07.151","volume":"609","author":"L Zhao","year":"2022","unstructured":"Zhao L, Wu H, Cao J (2022) Finite\/fixed-time bipartite consensus for networks of diffusion PDEs via event-triggered control. Inf Sci 609:1435\u20131450","journal-title":"Inf Sci"},{"issue":"17","key":"1430_CR9","doi-asserted-by":"publisher","first-page":"12808","DOI":"10.1016\/j.jfranklin.2020.09.031","volume":"357","author":"Q Liang","year":"2020","unstructured":"Liang Q, Wu Y, Hu J, Zhao Y (2020) Bipartite output synchronization of heterogeneous time-varying multi-agent systems via edge-based adaptive protocols. J Frankl Inst 357(17):12808\u201312824","journal-title":"J Frankl Inst"},{"issue":"1","key":"1430_CR10","doi-asserted-by":"publisher","first-page":"12","DOI":"10.1109\/TSMC.2023.3296880","volume":"54","author":"J Zhang","year":"2024","unstructured":"Zhang J, Zhang H, Sun S (2024) Adaptive dynamic event-triggered bipartite time-varying output formation tracking problem of heterogeneous multiagent systems. IEEE Trans Syst Man Cybern Syst 54(1):12\u201322","journal-title":"IEEE Trans Syst Man Cybern Syst"},{"issue":"9","key":"1430_CR11","doi-asserted-by":"publisher","first-page":"3887","DOI":"10.1109\/TAC.2020.2968876","volume":"65","author":"CN Hadjicostis","year":"2020","unstructured":"Hadjicostis CN, Dom\u00ednguez-Garc\u00eda AD (2020) Privacy-preserving distributed averaging via homomorphically encrypted ratio consensus. IEEE Trans Autom Control 65(9):3887\u20133894","journal-title":"IEEE Trans Autom Control"},{"key":"1430_CR12","doi-asserted-by":"publisher","DOI":"10.1016\/j.automatica.2022.110182","volume":"139","author":"K Zhang","year":"2022","unstructured":"Zhang K, Li Z, Wang Y, Louati A, Chen J (2022) Privacy-preserving dynamic average consensus via state decomposition: case study on multi-robot formation control. Automatica 139:110182","journal-title":"Automatica"},{"key":"1430_CR13","doi-asserted-by":"publisher","DOI":"10.1016\/j.automatica.2020.109253","volume":"122","author":"C Altafini","year":"2020","unstructured":"Altafini C (2020) A system-theoretic framework for privacy preservation in continuous-time multiagent dynamics. Automatica 122:109253","journal-title":"Automatica"},{"key":"1430_CR14","doi-asserted-by":"crossref","unstructured":"Huang Z, Mitra S, Dullerud G (2012) Differentially private iterative synchronous consensus. In: Proceedings of the 2012 ACM workshop on privacy in the electronic society, pp 81\u201390","DOI":"10.1145\/2381966.2381978"},{"key":"1430_CR15","doi-asserted-by":"crossref","unstructured":"Xu W, An J, Li H, Gan L, Yuen C (2024) Algorithm-unrolling-based distributed optimization for RIS-assisted cell-free networks. IEEE Internet Things J. 11:944\u2013957","DOI":"10.1109\/JIOT.2023.3288072"},{"key":"1430_CR16","doi-asserted-by":"crossref","unstructured":"Dwork C (2006) Differential privacy. In: Automata, languages and programming: 33rd international colloquium, ICALP 2006, Venice, Italy, July -10\u201314, 2006, proceedings, part II 33. Springer, pp 1\u201312","DOI":"10.1007\/11787006_1"},{"issue":"3","key":"1430_CR17","doi-asserted-by":"publisher","first-page":"3277","DOI":"10.1007\/s40747-022-00917-0","volume":"9","author":"C Xu","year":"2023","unstructured":"Xu C, Mei X, Liu D, Zhao K, Ding AS (2023) An efficient privacy-preserving point-of-interest recommendation model based on local differential privacy. Complex Intell Syst 9(3):3277\u20133300","journal-title":"Complex Intell Syst"},{"issue":"1","key":"1430_CR18","doi-asserted-by":"publisher","first-page":"60","DOI":"10.1109\/TCNS.2018.2795703","volume":"6","author":"L Gao","year":"2018","unstructured":"Gao L, Deng S, Ren W (2018) Differentially private consensus with an event-triggered mechanism. IEEE Trans Control Netw Syst 6(1):60\u201371","journal-title":"IEEE Trans Control Netw Syst"},{"key":"1430_CR19","doi-asserted-by":"publisher","first-page":"18","DOI":"10.1016\/j.automatica.2019.04.029","volume":"106","author":"D Fiore","year":"2019","unstructured":"Fiore D, Russo G (2019) Resilient consensus for multi-agent systems subject to differential privacy requirements. Automatica 106:18\u201326","journal-title":"Automatica"},{"issue":"12","key":"1430_CR20","doi-asserted-by":"publisher","first-page":"13915","DOI":"10.1109\/TCYB.2021.3135933","volume":"52","author":"Y Wang","year":"2022","unstructured":"Wang Y, Lam J, Lin H (2022) Consensus of linear multivariable discrete-time multiagent systems: differential privacy perspective. IEEE Trans Cybern 52(12):13915\u201313926","journal-title":"IEEE Trans Cybern"},{"issue":"3","key":"1430_CR21","first-page":"426","volume":"58","author":"J Ma","year":"2022","unstructured":"Ma J, Hu J (2022) Safe consensus control of cooperative-competitive multi-agent systems via differential privacy. Kybernetika 58(3):426\u2013439","journal-title":"Kybernetika"},{"issue":"4","key":"1430_CR22","doi-asserted-by":"publisher","first-page":"1655","DOI":"10.1016\/j.jfranklin.2022.01.024","volume":"359","author":"X Liu","year":"2022","unstructured":"Liu X, Wang Y, Xiao J, Chi M, Liu Z (2022) Concentrated differentially private average consensus algorithm for a discrete-time network with heterogeneous dynamics. J Frankl Inst 359(4):1655\u20131676","journal-title":"J Frankl Inst"},{"issue":"9","key":"1430_CR23","first-page":"3499","volume":"70","author":"X Wan","year":"2023","unstructured":"Wan X, Guo Y, Wu X (2023) Differentially private consensus for multi-agent systems under switching topology. IEEE Trans Circ Syst II Exp Briefs 70(9):3499\u20133503","journal-title":"IEEE Trans Circ Syst II Exp Briefs"},{"key":"1430_CR24","doi-asserted-by":"crossref","unstructured":"Wang Y, Lam J, Lin H (2023) Differentially private average consensus for networks with positive agents. IEEE Trans Cybern https:\/\/doi.org\/10.1109\/TCYB.2023.3267145","DOI":"10.1109\/TCYB.2023.3267145"},{"key":"1430_CR25","doi-asserted-by":"crossref","unstructured":"Wang J, Ke J, Zhang J-F (2024) Differentially private bipartite consensus over signed networks with time-varying noises. IEEE Trans Autom Control https:\/\/doi.org\/10.1109\/TAC.2024.3351869","DOI":"10.1109\/TAC.2024.3351869"},{"key":"1430_CR26","doi-asserted-by":"publisher","first-page":"26","DOI":"10.1016\/j.automatica.2018.03.020","volume":"93","author":"Y Wang","year":"2018","unstructured":"Wang Y, Liu X, Xiao J, Shen Y (2018) Output formation-containment of interacted heterogeneous linear systems by distributed hybrid active control. Automatica 93:26\u201332","journal-title":"Automatica"},{"issue":"7","key":"1430_CR27","doi-asserted-by":"publisher","first-page":"3045","DOI":"10.1109\/TCYB.2019.2926115","volume":"50","author":"Z-W Liu","year":"2019","unstructured":"Liu Z-W, Wen G, Yu X, Guan Z-H, Huang T (2019) Delayed impulsive control for consensus of multiagent systems with switching communication graphs. IEEE Trans Cybern 50(7):3045\u20133055","journal-title":"IEEE Trans Cybern"},{"key":"1430_CR28","doi-asserted-by":"publisher","DOI":"10.1016\/j.automatica.2023.110871","volume":"150","author":"Z Hu","year":"2023","unstructured":"Hu Z, Mu X (2023) Impulsive consensus of stochastic multi-agent systems under semi-Markovian switching topologies and application. Automatica 150:110871","journal-title":"Automatica"},{"key":"1430_CR29","doi-asserted-by":"publisher","DOI":"10.1016\/j.automatica.2020.109283","volume":"122","author":"X Liu","year":"2020","unstructured":"Liu X, Zhang J, Wang J (2020) Differentially private consensus algorithm for continuous-time heterogeneous multi-agent systems. Automatica 122:109283","journal-title":"Automatica"},{"issue":"1","key":"1430_CR30","doi-asserted-by":"publisher","first-page":"228","DOI":"10.1109\/TCYB.2020.2975234","volume":"52","author":"W Sun","year":"2020","unstructured":"Sun W, Zheng H, Guo W, Xu Y, Cao J, Abdel-Aty M, Chen S (2020) Quasisynchronization of heterogeneous dynamical networks via event-triggered impulsive controls. IEEE Trans Cybern 52(1):228\u2013239","journal-title":"IEEE Trans Cybern"},{"key":"1430_CR31","doi-asserted-by":"crossref","unstructured":"Chen R, Peng S (2023) Leader-follower quasi-consensus of multi-agent systems with packet loss using event-triggered impulsive control. Mathematics 11(13):2969","DOI":"10.3390\/math11132969"},{"key":"1430_CR32","doi-asserted-by":"crossref","unstructured":"Tang W, Liang C, Wu J, Xie Y (2023) Distributed impulsive control consensus for a class of unknown nonlinear multi-agent systems based on event-triggered scheme. Nonlinear Anal Hybrid Syst 49:101352","DOI":"10.1016\/j.nahs.2023.101352"},{"issue":"3","key":"1430_CR33","doi-asserted-by":"publisher","first-page":"1836","DOI":"10.1109\/TCYB.2020.2999359","volume":"52","author":"Z Zhang","year":"2020","unstructured":"Zhang Z, Peng S, Liu D, Wang Y, Chen T (2020) Leader-following mean-square consensus of stochastic multiagent systems with ROUs and RONs via distributed event-triggered impulsive control. IEEE Trans Cybern 52(3):1836\u20131849","journal-title":"IEEE Trans Cybern"},{"key":"1430_CR34","doi-asserted-by":"publisher","first-page":"414","DOI":"10.1016\/j.ins.2022.08.086","volume":"612","author":"L Zhang","year":"2022","unstructured":"Zhang L, Li Y, Lu J, Lou J (2022) Bipartite event-triggered impulsive output consensus for switching multi-agent systems with dynamic leader. Inf Sci 612:414\u2013426","journal-title":"Inf Sci"},{"key":"1430_CR35","doi-asserted-by":"publisher","first-page":"1128","DOI":"10.1016\/j.ins.2022.11.132","volume":"622","author":"W Li","year":"2023","unstructured":"Li W, Sader M, Zhu Z, Liu Z, Chen Z (2023) Event-triggered fault-tolerant secure containment control of multi-agent systems through impulsive scheme. Inf Sci 622:1128\u20131140","journal-title":"Inf Sci"},{"key":"1430_CR36","doi-asserted-by":"publisher","first-page":"11","DOI":"10.1016\/j.neucom.2021.10.019","volume":"468","author":"Z Zuo","year":"2022","unstructured":"Zuo Z, Tian R, Han Q, Wang Y, Zhang W (2022) Differential privacy for bipartite consensus over signed digraph. Neurocomputing 468:11\u201321","journal-title":"Neurocomputing"},{"issue":"4","key":"1430_CR37","doi-asserted-by":"publisher","first-page":"935","DOI":"10.1109\/TAC.2012.2224251","volume":"58","author":"C Altafini","year":"2012","unstructured":"Altafini C (2012) Consensus problems on networks with antagonistic interactions. IEEE Trans Autom Control 58(4):935\u2013946","journal-title":"IEEE Trans Autom Control"},{"key":"1430_CR38","doi-asserted-by":"publisher","first-page":"123","DOI":"10.1016\/j.ejcon.2021.03.002","volume":"59","author":"Y Wu","year":"2021","unstructured":"Wu Y, Liang Q, Zhao Y, Hu J, Xiang L (2021) Adaptive bipartite consensus control of general linear multi-agent systems using noisy measurements. Eur J Control 59:123\u2013128","journal-title":"Eur J Control"},{"key":"1430_CR39","doi-asserted-by":"publisher","first-page":"1350","DOI":"10.1109\/TCSI.2022.3226578","volume":"70","author":"Q Luo","year":"2022","unstructured":"Luo Q, Liu S, Wang L, Tian E (2022) Privacy-preserved distributed optimization for multi-agent systems with antagonistic interactions. IEEE Trans Circ Syst I Reg Pap 70:1350\u20131360","journal-title":"IEEE Trans Circ Syst I Reg Pap"},{"issue":"4","key":"1430_CR40","first-page":"1062","volume":"57","author":"Y Su","year":"2011","unstructured":"Su Y, Huang J (2011) Cooperative output regulation of linear multi-agent systems. IEEE Trans Autom Control 57(4):1062\u20131066","journal-title":"IEEE Trans Autom Control"}],"container-title":["Complex &amp; Intelligent Systems"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s40747-024-01430-2.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s40747-024-01430-2\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s40747-024-01430-2.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,7,17]],"date-time":"2024-07-17T17:20:46Z","timestamp":1721236846000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s40747-024-01430-2"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,4,17]]},"references-count":40,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2024,8]]}},"alternative-id":["1430"],"URL":"https:\/\/doi.org\/10.1007\/s40747-024-01430-2","relation":{},"ISSN":["2199-4536","2198-6053"],"issn-type":[{"value":"2199-4536","type":"print"},{"value":"2198-6053","type":"electronic"}],"subject":[],"published":{"date-parts":[[2024,4,17]]},"assertion":[{"value":"5 December 2023","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"23 March 2024","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"17 April 2024","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"No potential conflict of interest was reported by the authors.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}}]}}