{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,22]],"date-time":"2026-05-22T12:10:40Z","timestamp":1779451840673,"version":"3.53.1"},"reference-count":55,"publisher":"Elsevier BV","license":[{"start":{"date-parts":[[2026,5,1]],"date-time":"2026-05-01T00:00:00Z","timestamp":1777593600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/tdm\/userlicense\/1.0\/"},{"start":{"date-parts":[[2026,5,1]],"date-time":"2026-05-01T00:00:00Z","timestamp":1777593600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/legal\/tdmrep-license"},{"start":{"date-parts":[[2026,5,1]],"date-time":"2026-05-01T00:00:00Z","timestamp":1777593600000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-017"},{"start":{"date-parts":[[2026,5,1]],"date-time":"2026-05-01T00:00:00Z","timestamp":1777593600000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-037"},{"start":{"date-parts":[[2026,5,1]],"date-time":"2026-05-01T00:00:00Z","timestamp":1777593600000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-012"},{"start":{"date-parts":[[2026,5,1]],"date-time":"2026-05-01T00:00:00Z","timestamp":1777593600000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-029"},{"start":{"date-parts":[[2026,5,1]],"date-time":"2026-05-01T00:00:00Z","timestamp":1777593600000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-004"}],"funder":[{"DOI":"10.13039\/501100002858","name":"China Postdoctoral Science Foundation","doi-asserted-by":"publisher","award":["2024M753837"],"award-info":[{"award-number":["2024M753837"]}],"id":[{"id":"10.13039\/501100002858","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100005230","name":"Natural Science Foundation of Chongqing Municipality","doi-asserted-by":"publisher","award":["CSTB2024NSCQ-MSX0955"],"award-info":[{"award-number":["CSTB2024NSCQ-MSX0955"]}],"id":[{"id":"10.13039\/501100005230","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100012226","name":"Fundamental Research Funds for the Central Universities","doi-asserted-by":"publisher","award":["2025CDJZDGF001"],"award-info":[{"award-number":["2025CDJZDGF001"]}],"id":[{"id":"10.13039\/501100012226","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["62506053"],"award-info":[{"award-number":["62506053"]}],"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":["61932006"],"award-info":[{"award-number":["61932006"]}],"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":["62302068"],"award-info":[{"award-number":["62302068"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100012669","name":"Natural Science Foundation Project of Chongqing","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100012669","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["elsevier.com","sciencedirect.com"],"crossmark-restriction":true},"short-container-title":["Knowledge-Based Systems"],"published-print":{"date-parts":[[2026,5]]},"DOI":"10.1016\/j.knosys.2026.115812","type":"journal-article","created":{"date-parts":[[2026,3,21]],"date-time":"2026-03-21T00:17:01Z","timestamp":1774052221000},"page":"115812","update-policy":"https:\/\/doi.org\/10.1016\/elsevier_cm_policy","source":"Crossref","is-referenced-by-count":0,"special_numbering":"C","title":["Dynamics-based algorithm-level privacy preservation for push-sum average consensus"],"prefix":"10.1016","volume":"341","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-4004-8490","authenticated-orcid":false,"given":"Huqiang","family":"Cheng","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0434-202X","authenticated-orcid":false,"given":"Mengying","family":"Xie","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1512-487X","authenticated-orcid":false,"given":"Xiaowei","family":"Yang","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3602-0946","authenticated-orcid":false,"given":"Qingguo","family":"L\u00fc","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6310-8965","authenticated-orcid":false,"given":"Huaqing","family":"Li","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"78","reference":[{"key":"10.1016\/j.knosys.2026.115812_bib0001","doi-asserted-by":"crossref","DOI":"10.1016\/j.knosys.2021.107549","article-title":"How to get consensus with neighbors?\u201d: rating standardization for accurate collaborative filtering","volume":"234","author":"Bae","year":"2021","journal-title":"Knowl.Based Syst."},{"key":"10.1016\/j.knosys.2026.115812_bib0002","doi-asserted-by":"crossref","first-page":"101","DOI":"10.1016\/j.knosys.2011.08.011","article-title":"Consensus clustering based on constrained self-organizing map and improved cop-Kmeans ensemble in intelligent decision support systems","volume":"32","author":"Yang","year":"2012","journal-title":"Knowl. Based Syst."},{"key":"10.1016\/j.knosys.2026.115812_bib0003","doi-asserted-by":"crossref","DOI":"10.1016\/j.knosys.2020.106240","article-title":"Consensus reaching for social network group decision making by considering leadership and bounded confidence","volume":"204","author":"Zhang","year":"2020","journal-title":"Knowl. Based Syst."},{"key":"10.1016\/j.knosys.2026.115812_bib0004","series-title":"Proceedings of the IEEE International Systems Conference","first-page":"1","article-title":"Influence of network topology on UAVs formation control based on distributed consensus","author":"Souza","year":"2022"},{"key":"10.1016\/j.knosys.2026.115812_bib0005","doi-asserted-by":"crossref","DOI":"10.1016\/j.knosys.2024.112582","article-title":"Stabilized distributed online mirror descent for multi-agent optimization","volume":"304","author":"Wu","year":"2024","journal-title":"Knowl. Based Syst."},{"key":"10.1016\/j.knosys.2026.115812_bib0006","series-title":"Proceedings of 44th Annual IEEE Symposium on Foundations of Computer Science","first-page":"482","article-title":"Gossip-based computation of aggregate information","author":"Kempe","year":"2003"},{"key":"10.1016\/j.knosys.2026.115812_bib0007","doi-asserted-by":"crossref","DOI":"10.1016\/j.knosys.2023.110531","article-title":"Dynamic asynchronous edge-based event-triggered consensus of multi-agent systems","volume":"272","author":"Xia","year":"2023","journal-title":"Knowl. Based Syst."},{"key":"10.1016\/j.knosys.2026.115812_bib0008","series-title":"Proceedings of 2010IEEE International Symposium on Information Theory","first-page":"1753","article-title":"Weighted gossip: distributed averaging using non-doubly stochastic matrices","author":"B\u00e9n\u00e9zit","year":"2010"},{"issue":"2\u20133","key":"10.1016\/j.knosys.2026.115812_bib0009","doi-asserted-by":"crossref","first-page":"99","DOI":"10.1561\/2600000016","article-title":"Distributed averaging and balancing in network systems: with applications to coordination and control","volume":"5","author":"Hadjicostis","year":"2018","journal-title":"Found. Trends Syst. Contr."},{"key":"10.1016\/j.knosys.2026.115812_bib0010","doi-asserted-by":"crossref","DOI":"10.1016\/j.knosys.2024.111430","article-title":"A novel data-driven model-free synchronization protocol for discrete-time multi-agent systems via TD3 based algorithm","volume":"287","author":"Liu","year":"2024","journal-title":"Knowl. Based Syst."},{"key":"10.1016\/j.knosys.2026.115812_bib0011","doi-asserted-by":"crossref","DOI":"10.1016\/j.knosys.2024.111710","article-title":"Multi-dimensional multi-round minimum cost consensus models with iterative mechanisms involving reward and punishment measures","volume":"293","author":"Guo","year":"2024","journal-title":"Knowl. Based Syst."},{"key":"10.1016\/j.knosys.2026.115812_bib0012","series-title":"Technical Report","article-title":"Problems in decentralized decision making and computation","author":"Tsitsiklis","year":"1984"},{"key":"10.1016\/j.knosys.2026.115812_bib0013","series-title":"Proceedings of the IEEE Power and Energy Society General Meeting","first-page":"1","article-title":"Incremental cost consensus algorithm in a smart grid environment","author":"Zhang","year":"2011"},{"key":"10.1016\/j.knosys.2026.115812_bib0014","doi-asserted-by":"crossref","DOI":"10.1016\/j.sysconle.2020.104869","article-title":"Secure and privacy preserving consensus for second-order systems based on paillier encryption","volume":"148","author":"Fang","year":"2021","journal-title":"Syst. Contr. Lett."},{"issue":"10","key":"10.1016\/j.knosys.2026.115812_bib0015","doi-asserted-by":"crossref","first-page":"4035","DOI":"10.1109\/TAC.2019.2890887","article-title":"Secure and privacy-preserving consensus","volume":"64","author":"Ruan","year":"2019","journal-title":"IEEE Trans. Autom. Contr."},{"issue":"4","key":"10.1016\/j.knosys.2026.115812_bib0016","first-page":"690","article-title":"Accurate privacy preserving average consensus","volume":"67","author":"Yin","year":"2019","journal-title":"IEEE Trans. Circuits Syst. II Express Briefs"},{"issue":"3","key":"10.1016\/j.knosys.2026.115812_bib0017","first-page":"1104","article-title":"Multi-dimensional privacy-preserving average consensus in wireless sensor networks","volume":"69","author":"Yu","year":"2021","journal-title":"IEEE Trans. Circuits Syst. II Express Briefs"},{"key":"10.1016\/j.knosys.2026.115812_bib0018","series-title":"Proceedings of the 3rd Theory Cryptography Conference","first-page":"265","article-title":"Calibrating noise to sensitivity in private data analysis","author":"Dwork","year":"2006"},{"key":"10.1016\/j.knosys.2026.115812_bib0019","doi-asserted-by":"crossref","first-page":"221","DOI":"10.1016\/j.automatica.2017.03.016","article-title":"Differentially private average consensus: obstructions, trade-offs, and optimal algorithm design","volume":"81","author":"Nozari","year":"2017","journal-title":"Automatica"},{"key":"10.1016\/j.knosys.2026.115812_bib0020","series-title":"Proceedings of the 2012","first-page":"81","article-title":"Differentially private iterative synchronous consensus","author":"Huang","year":"2012"},{"issue":"8","key":"10.1016\/j.knosys.2026.115812_bib0021","doi-asserted-by":"crossref","first-page":"4075","DOI":"10.1109\/TCYB.2018.2890645","article-title":"Differentially private consensus with quantized communication","volume":"51","author":"Gao","year":"2021","journal-title":"IEEE Trans. Cybern."},{"issue":"10","key":"10.1016\/j.knosys.2026.115812_bib0022","doi-asserted-by":"crossref","first-page":"4214","DOI":"10.1109\/TCYB.2019.2906574","article-title":"Differentially private malicious agent avoidance in multiagent advising learning","volume":"50","author":"Ye","year":"2020","journal-title":"IEEE Trans. Cybern."},{"issue":"4","key":"10.1016\/j.knosys.2026.115812_bib0023","doi-asserted-by":"crossref","first-page":"5523","DOI":"10.1109\/TNNLS.2022.3207470","article-title":"Differentially private consensus for second-order multiagent systems with quantized communication","volume":"35","author":"Zhang","year":"2024","journal-title":"IEEE Trans. Neural Netw. Learn. Syst."},{"issue":"10","key":"10.1016\/j.knosys.2026.115812_bib0024","doi-asserted-by":"crossref","first-page":"6725","DOI":"10.1109\/TCYB.2022.3233296","article-title":"Differentially private average consensus with logarithmic dynamic encoding-decoding scheme","volume":"53","author":"Chen","year":"2023","journal-title":"IEEE Trans. Cybern."},{"issue":"6","key":"10.1016\/j.knosys.2026.115812_bib0025","doi-asserted-by":"crossref","first-page":"3454","DOI":"10.1109\/TCYB.2023.3267145","article-title":"Differentially private average consensus for networks with positive agents","volume":"54","author":"Wang","year":"2024","journal-title":"IEEE Trans. Cybern."},{"key":"10.1016\/j.knosys.2026.115812_bib0026","series-title":"IEEE International Conference on Telecommunications and Malaysia International Conference on Communications","first-page":"556","article-title":"Secure consensus averaging in sensor networks using random offsets","author":"Kefayati","year":"2007"},{"issue":"2","key":"10.1016\/j.knosys.2026.115812_bib0027","doi-asserted-by":"crossref","first-page":"753","DOI":"10.1109\/TAC.2016.2564339","article-title":"Privacy preserving average consensus","volume":"62","author":"Mo","year":"2017","journal-title":"IEEE Trans. Autom. Contr."},{"key":"10.1016\/j.knosys.2026.115812_bib0028","series-title":"European Control Conference (ECC)","first-page":"760","article-title":"Privacy-preserving asymptotic average consensus","author":"Manitara","year":"2013"},{"key":"10.1016\/j.knosys.2026.115812_bib0029","series-title":"Proceedings of the 53rd IEEE Conference on Decision and Control","first-page":"1370","article-title":"Design of communication networks for distributed computation with privacy guarantees","author":"Pequito","year":"2014"},{"key":"10.1016\/j.knosys.2026.115812_bib0030","series-title":"Proceedings of IEEE 57th Annual Allerton Conference on Communication, Control, and Computing","first-page":"446","article-title":"Simple, private, and accurate distributed averaging","author":"Ridgley","year":"2019"},{"key":"10.1016\/j.knosys.2026.115812_bib0031","series-title":"Proceedings of American Control Conference","first-page":"4460","article-title":"Adaptive communication networks with privacy guarantees","author":"Alaeddini","year":"2017"},{"issue":"11","key":"10.1016\/j.knosys.2026.115812_bib0032","doi-asserted-by":"crossref","first-page":"4711","DOI":"10.1109\/TAC.2019.2902731","article-title":"Privacy-preserving average consensus via state decomposition","volume":"64","author":"Wang","year":"2019","journal-title":"IEEE Trans. Autom. Contr."},{"key":"10.1016\/j.knosys.2026.115812_bib0033","doi-asserted-by":"crossref","DOI":"10.1016\/j.automatica.2022.110182","article-title":"Privacy-preserving dynamic average consensus via state decomposition: case study on multi-robot formation control","volume":"139","author":"Zhang","year":"2022","journal-title":"Automatica"},{"issue":"9","key":"10.1016\/j.knosys.2026.115812_bib0034","doi-asserted-by":"crossref","first-page":"3887","DOI":"10.1109\/TAC.2020.2968876","article-title":"Privacy-preserving distributed averaging via homomorphically encrypted ratio consensus","volume":"65","author":"Hadjicostis","year":"2020","journal-title":"IEEE Trans. Autom. Contr."},{"key":"10.1016\/j.knosys.2026.115812_bib0035","doi-asserted-by":"crossref","first-page":"87","DOI":"10.1016\/j.neucom.2021.06.016","article-title":"Differentially private average consensus with general directed graphs","volume":"458","author":"Wang","year":"2021","journal-title":"Neurocomputing"},{"issue":"12","key":"10.1016\/j.knosys.2026.115812_bib0036","doi-asserted-by":"crossref","first-page":"7974","DOI":"10.1109\/TAC.2023.3256479","article-title":"Privacy-preserving push-sum average consensus via state decomposition","volume":"68","author":"Chen","year":"2023","journal-title":"IEEE Trans. Autom. Contr."},{"issue":"1","key":"10.1016\/j.knosys.2026.115812_bib0037","doi-asserted-by":"crossref","first-page":"1029","DOI":"10.1109\/TCNS.2024.3431730","article-title":"Dynamic-based privacy preservation for distributed economic dispatch of microgrids","volume":"12","author":"Cheng","year":"2024","journal-title":"IEEE Trans. Contr. Netw. Syst"},{"key":"10.1016\/j.knosys.2026.115812_bib0038","series-title":"IEEE Conference on Communications and Network Security (CNS)","first-page":"1","article-title":"Privacy-preserving average consensus on directed graphs using push-sum","author":"Gao","year":"2018"},{"issue":"2","key":"10.1016\/j.knosys.2026.115812_bib0039","doi-asserted-by":"crossref","first-page":"918","DOI":"10.1109\/TNSE.2022.3140274","article-title":"Algorithm-level confidentiality for average consensus on time-varying directed graphs","volume":"9","author":"Gao","year":"2022","journal-title":"IEEE Trans. Netw. Sci. Eng."},{"key":"10.1016\/j.knosys.2026.115812_bib0040","series-title":"Proceedings of the 41st Chinese Control Conference","first-page":"4955","article-title":"Dynamics based privacy preservation for average consensus on directed graphs","author":"Liu","year":"2022"},{"key":"10.1016\/j.knosys.2026.115812_bib0041","first-page":"1","article-title":"Privacy preserving distributed average consensus on time-varying directed graphs","volume":"0","author":"Gao","year":"2025","journal-title":"Int. J. Robust Nonlinear Contr."},{"key":"10.1016\/j.knosys.2026.115812_bib0042","article-title":"A fully decentralized distributed learning algorithm for latency communication networks","volume":"309","author":"Wei","year":"2024","journal-title":"Knowl. Based Syst."},{"key":"10.1016\/j.knosys.2026.115812_bib0043","series-title":"Annual American Control Conference (ACC)","first-page":"1402","article-title":"Private optimization on networks","author":"Gade","year":"2018"},{"key":"10.1016\/j.knosys.2026.115812_bib0044","first-page":"513","article-title":"Privacy-preserving push-pull method for decentralized optimization via state decomposition","volume":"10","author":"Cheng","year":"2024","journal-title":"IEEE Trans. Signal Inf. Proc. Netw."},{"key":"10.1016\/j.knosys.2026.115812_bib0045","doi-asserted-by":"crossref","DOI":"10.1016\/j.automatica.2023.110878","article-title":"Dynamics based privacy preservation in decentralized optimization","volume":"151","author":"Gao","year":"2023","journal-title":"Automatica"},{"issue":"2","key":"10.1016\/j.knosys.2026.115812_bib0046","doi-asserted-by":"crossref","first-page":"1716","DOI":"10.1109\/TNSE.2023.3329832","article-title":"Distributed online private learning of convex nondecomposable objectives","volume":"11","author":"Cheng","year":"2024","journal-title":"IEEE Trans. Netw. Sci. Eng."},{"issue":"1","key":"10.1016\/j.knosys.2026.115812_bib0047","first-page":"92","article-title":"Random projection-based multiplicative data perturbation for privacy preserving distributed data mining","volume":"18","author":"Liu","year":"2005","journal-title":"IEEE Trans Knowl. Data Eng."},{"issue":"6","key":"10.1016\/j.knosys.2026.115812_bib0048","doi-asserted-by":"crossref","first-page":"884","DOI":"10.1109\/TKDE.2009.153","article-title":"Privacy-preserving gradient-descent methods","volume":"22","author":"Han","year":"2009","journal-title":"IEEE Trans Knowl. Data Eng."},{"issue":"1","key":"10.1016\/j.knosys.2026.115812_bib0049","doi-asserted-by":"crossref","first-page":"222","DOI":"10.1109\/TPDS.2013.45","article-title":"Privacy-preserving multi-keyword ranked search over encrypted cloud data","volume":"25","author":"Cao","year":"2013","journal-title":"IEEE Trans. Parallel Distrib. Syst."},{"key":"10.1016\/j.knosys.2026.115812_bib0050","series-title":"Non-negative Matrices and Markov Chains","author":"Seneta","year":"1973"},{"issue":"1","key":"10.1016\/j.knosys.2026.115812_bib0051","doi-asserted-by":"crossref","first-page":"62","DOI":"10.1214\/aoap\/1177005981","article-title":"Eigenvalue bounds on convergence to stationarity for nonreversible markov chains with an application to the exclusion process","volume":"1","author":"Fill","year":"1991","journal-title":"Ann. Appl. Probab."},{"key":"10.1016\/j.knosys.2026.115812_bib0052","series-title":"Matrix Analysis","author":"Horn","year":"2012"},{"key":"10.1016\/j.knosys.2026.115812_bib0053","doi-asserted-by":"crossref","DOI":"10.1016\/j.automatica.2020.108839","article-title":"On privacy preserving data release of linear dynamic networks","volume":"115","author":"Lu","year":"2020","journal-title":"Automatica"},{"key":"10.1016\/j.knosys.2026.115812_bib0054","first-page":"3","volume":"1","author":"Machanavajjhala","year":"2007","journal-title":"L-diversity: privacy beyond k-anonymity"},{"issue":"4","key":"10.1016\/j.knosys.2026.115812_bib0055","doi-asserted-by":"crossref","first-page":"922","DOI":"10.1109\/TAC.2010.2041686","article-title":"Constrained consensus and optimization in multi-agent networks","volume":"55","author":"Nedi\u0107","year":"2010","journal-title":"IEEE Trans. Autom. Contr."}],"container-title":["Knowledge-Based Systems"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0950705126005381?httpAccept=text\/xml","content-type":"text\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0950705126005381?httpAccept=text\/plain","content-type":"text\/plain","content-version":"vor","intended-application":"text-mining"}],"deposited":{"date-parts":[[2026,5,22]],"date-time":"2026-05-22T11:44:51Z","timestamp":1779450291000},"score":1,"resource":{"primary":{"URL":"https:\/\/linkinghub.elsevier.com\/retrieve\/pii\/S0950705126005381"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,5]]},"references-count":55,"alternative-id":["S0950705126005381"],"URL":"https:\/\/doi.org\/10.1016\/j.knosys.2026.115812","relation":{},"ISSN":["0950-7051"],"issn-type":[{"value":"0950-7051","type":"print"}],"subject":[],"published":{"date-parts":[[2026,5]]},"assertion":[{"value":"Elsevier","name":"publisher","label":"This article is maintained by"},{"value":"Dynamics-based algorithm-level privacy preservation for push-sum average consensus","name":"articletitle","label":"Article Title"},{"value":"Knowledge-Based Systems","name":"journaltitle","label":"Journal Title"},{"value":"https:\/\/doi.org\/10.1016\/j.knosys.2026.115812","name":"articlelink","label":"CrossRef DOI link to publisher maintained version"},{"value":"article","name":"content_type","label":"Content Type"},{"value":"\u00a9 2026 Elsevier B.V. All rights are reserved, including those for text and data mining, AI training, and similar technologies.","name":"copyright","label":"Copyright"}],"article-number":"115812"}}