{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T04:10:34Z","timestamp":1760242234513,"version":"build-2065373602"},"reference-count":28,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2017,1,13]],"date-time":"2017-01-13T00:00:00Z","timestamp":1484265600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"the Strategic Priority Research Program of the Chinese Academy of Sciences","award":["XDA06020500"],"award-info":[{"award-number":["XDA06020500"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>Time synchronization is one of the key technologies in Industrial Wireless Sensor Networks (IWSNs), and clustering is widely used in WSNs for data fusion and information collection to reduce redundant data and communication overhead. Considering IWSNs\u2019 demand for low energy consumption, fast convergence, and robustness, this paper presents a novel Cluster-based Maximum consensus Time Synchronization (CMTS) method. It consists of two parts: intra-cluster time synchronization and inter-cluster time synchronization. Based on the theory of distributed consensus, the proposed method utilizes the maximum consensus approach to realize the intra-cluster time synchronization, and adjacent clusters exchange the time messages via overlapping nodes to synchronize with each other. A Revised-CMTS is further proposed to counteract the impact of bounded communication delays between two connected nodes, because the traditional stochastic models of the communication delays would distort in a dynamic environment. The simulation results show that our method reduces the communication overhead and improves the convergence rate in comparison to existing works, as well as adapting to the uncertain bounded communication delays.<\/jats:p>","DOI":"10.3390\/s17010141","type":"journal-article","created":{"date-parts":[[2017,1,13]],"date-time":"2017-01-13T10:08:37Z","timestamp":1484302117000},"page":"141","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":31,"title":["Cluster-Based Maximum Consensus Time Synchronization for Industrial Wireless Sensor Networks"],"prefix":"10.3390","volume":"17","author":[{"given":"Zhaowei","family":"Wang","sequence":"first","affiliation":[{"name":"Key Laboratory of Networked Control System, Shenyang Institute of Automation, Chinese Academy of Sciences, Shenyang 110016, China"},{"name":"University of Chinese Academy of Sciences, Beijing 100049, China"}]},{"given":"Peng","family":"Zeng","sequence":"additional","affiliation":[{"name":"Key Laboratory of Networked Control System, Shenyang Institute of Automation, Chinese Academy of Sciences, Shenyang 110016, China"}]},{"given":"Mingtuo","family":"Zhou","sequence":"additional","affiliation":[{"name":"Key Laboratory of Wireless Sensor Network &amp; Communication, Shanghai Institute of Microsystem Information and Technology, Chinese Academy of Sciences, Shanghai 200050, China"},{"name":"Shanghai Research Center for Wireless Communications, Shanghai 201210, China"}]},{"given":"Dong","family":"Li","sequence":"additional","affiliation":[{"name":"Key Laboratory of Networked Control System, Shenyang Institute of Automation, Chinese Academy of Sciences, Shenyang 110016, China"}]},{"given":"Jintao","family":"Wang","sequence":"additional","affiliation":[{"name":"Key Laboratory of Networked Control System, Shenyang Institute of Automation, Chinese Academy of Sciences, Shenyang 110016, China"},{"name":"University of Chinese Academy of Sciences, Beijing 100049, China"}]}],"member":"1968","published-online":{"date-parts":[[2017,1,13]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Wang, Z.-W., Zeng, P., Zhou, M.-T., and Li, D. (2016, January 15\u201318). Cluster-based maximum consensus time synchronization in IWSNs. Proceedings of the IEEE 83rd Vehicular Technology Conference-Spring, Nanjing, China.","DOI":"10.1109\/VTCSpring.2016.7504162"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"860","DOI":"10.1109\/SURV.2012.071812.00124","article-title":"Introduction to industrial control networks","volume":"15","author":"Gallloway","year":"2012","journal-title":"IEEE Commun. Surv. Tutor."},{"key":"ref_3","first-page":"152","article-title":"Joint routing and scheduling optimization in industrial wireless networks using an extremal dynamics algorithm","volume":"43","author":"He","year":"2014","journal-title":"Inf. Control"},{"key":"ref_4","first-page":"1008","article-title":"Simsync: A time synchronization simulator for sensor networks","volume":"32","author":"Xu","year":"2006","journal-title":"Acta Autom. Sin."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"873","DOI":"10.3724\/SP.J.1004.2010.00873","article-title":"A fast averaging synchronization algorithm for clock oscillators in nonlinear dynamical network with arbitrary time-delays","volume":"36","author":"Chen","year":"2010","journal-title":"Acta Autom. Sin."},{"key":"ref_6","first-page":"753","article-title":"An energy-efficient time synchronization algorithm for wireless sensor networks","volume":"40","author":"Wang","year":"2011","journal-title":"Inf. Control"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"147","DOI":"10.1145\/844128.844143","article-title":"Fine-grained network time synchronization using reference broadcasts","volume":"36","author":"Elson","year":"2002","journal-title":"ACM SIGOPS Oper. Syst. Rev."},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"Ganeriwal, S., Kumar, P., and Srivastava, M.B. (2003, January 5\u20137). Timing-sync protocol for sensor networks. Proceedings of the 1st International Conference on Embedded Networked Sensor Systems, Los Angeles, CA, USA.","DOI":"10.1145\/958491.958508"},{"key":"ref_9","doi-asserted-by":"crossref","unstructured":"Maroti, M., Kusy, B., Simon, G., and Ledeczi, A. (2004, January 3\u20135). The flooding time synchronization protocol. Proceedings of the 2nd International Conference on Embedded Networked Sensor Systems, Baltimore, MD, USA.","DOI":"10.1145\/1031495.1031501"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"244","DOI":"10.1109\/TPDS.2013.40","article-title":"Time synchronization based on slow-flooding in wireless sensor networks","volume":"25","author":"Yildirim","year":"2014","journal-title":"IEEE Trans. Parallel Distrib. Syst."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"7625","DOI":"10.3390\/s110807625","article-title":"Enhanced precision time synchronization for wireless sensor networks","volume":"11","author":"Cho","year":"2011","journal-title":"Sensors"},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"He, J.-P., Cheng, P., Shi, L., and Chen, J.-M. (2011, January 12\u201315). Time synchronization in WSNs: a maximum-value-based consensus approach. Proceedings of the 2011 50th IEEE Conference on Decision and Control and European Control Conference, Orlando, FL, USA.","DOI":"10.1109\/CDC.2011.6161443"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"14744","DOI":"10.3390\/s140814744","article-title":"A group neighborhood average clock synchronization protocol for wireless sensor networks","volume":"14","author":"Lin","year":"2014","journal-title":"Sensors"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"2440","DOI":"10.1109\/LSP.2015.2491320","article-title":"Clock skew estimation of listening nodes with clock correction upon every synchronization in wireless sensor networks","volume":"22","author":"Wang","year":"2015","journal-title":"IEEE Signal Process. Lett."},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Sun, W., Brannstrom, F., and Strom, E.G. (2013, January 9\u201313). On clock offset and skew estimation with exponentially distributed delays. Proceedings of the IEEE International Conference on Communications, Budapest, Hungary.","DOI":"10.1109\/ICC.2013.6654794"},{"key":"ref_16","unstructured":"Yadav, P., Yadav, N., and Varma, S. (2007, January 17\u201319). Cluster based hierarchical wireless sensor networks (CHWSN) and time synchronization in CHWSN. Proceedings of the IEEE International Symposium on Communications and Information Technologies (ISCIT), Sydney, Australia."},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"Kong, L., Wang, Q., and Zhao, Y. (2010, January 16\u201318). Time synchronization algorithm based on cluster for wsn. Proceedings of the 2nd IEEE International Conference on Information Management and Engineering (ICIME), Chengdu, China.","DOI":"10.1109\/ICIME.2010.5477523"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"1404","DOI":"10.1109\/JSEN.2014.2363471","article-title":"Cluster-based consensus time synchronization for wireless sensor networks","volume":"15","author":"Wu","year":"2015","journal-title":"IEEE Sens. J."},{"key":"ref_19","doi-asserted-by":"crossref","unstructured":"Garone, E., Gasparri, A., and Lamonaca, F. (2013, January 17\u201319). Clock synchronization for wireless sensor network with communication delay. Proceedings of the American Control Conference, Washington, DC, USA.","DOI":"10.1109\/ACC.2013.6579929"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"60","DOI":"10.1016\/j.automatica.2015.06.014","article-title":"Clock synchronization protocol for wireless sensor networks with bounded communication delays","volume":"59","author":"Garone","year":"2015","journal-title":"Automatica"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"1878","DOI":"10.1016\/j.automatica.2011.06.012","article-title":"Average timesynch: A consensus-based protocol for clock synchronization in wireless sensor networks","volume":"47","author":"Schenato","year":"2011","journal-title":"Automatica"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"575","DOI":"10.1007\/s11045-013-0276-x","article-title":"Model approximation for two-dimensional Markovian jump systems with state-delays and imperfect mode information","volume":"26","author":"Wei","year":"2015","journal-title":"Multidimens. Syst. Signal Process."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"316","DOI":"10.1016\/j.ins.2013.12.042","article-title":"Filtering design for two-dimensional Markovian jump systems with state-delays and deficient mode information","volume":"269","author":"Wei","year":"2014","journal-title":"Inf. Sci."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"52","DOI":"10.1016\/j.nahs.2014.11.003","article-title":"Mode-dependent nonrational output feedback control for continuous-time semi-Markovian jump systems with time-varying delay","volume":"16","author":"Wei","year":"2015","journal-title":"Nonlinear Anal. Hybrid Syst."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"656","DOI":"10.1002\/oca.2093","article-title":"New results on \n          \n            \n              \n\t\t\t  \n                H\n                  \u221e\n                \n              \n            \n          \n         dynamic output feedback control for Markovian jump systems with time-varying delay and defective mode information","volume":"35","author":"Wei","year":"2014","journal-title":"Optim. Control Appl. Methods"},{"key":"ref_26","doi-asserted-by":"crossref","unstructured":"He, J.-P., Duan, X.-M., Cheng, P., Shi, L., and Cai, L. (2014, January 15\u201317). Distributed time synchronization under bounded noise in wireless sensor networks. Proceedings of the IEEE 53rd Annual Conference on Decision and Control, Los Angeles, CA, USA.","DOI":"10.1109\/CDC.2014.7040470"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"347","DOI":"10.1016\/j.isatra.2013.11.001","article-title":"Study of consensus-based time synchronization in wireless sensor networks","volume":"53","author":"He","year":"2014","journal-title":"ISA Trans."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"2269","DOI":"10.1109\/JSEN.2011.2182045","article-title":"Consensus clock synchronization for wirelss sensor networks","volume":"12","author":"Maggs","year":"2012","journal-title":"IEEE Sens. J."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/17\/1\/141\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T18:26:07Z","timestamp":1760207167000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/17\/1\/141"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,1,13]]},"references-count":28,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2017,1]]}},"alternative-id":["s17010141"],"URL":"https:\/\/doi.org\/10.3390\/s17010141","relation":{},"ISSN":["1424-8220"],"issn-type":[{"type":"electronic","value":"1424-8220"}],"subject":[],"published":{"date-parts":[[2017,1,13]]}}}