{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T04:46:49Z","timestamp":1760244409527,"version":"build-2065373602"},"reference-count":27,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2022,12,22]],"date-time":"2022-12-22T00:00:00Z","timestamp":1671667200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Natural Science Foundation of the Jiangsu Higher Education Institutions of China","award":["17KJB510051","KX-22-B60","2021GRFX068"],"award-info":[{"award-number":["17KJB510051","KX-22-B60","2021GRFX068"]}]},{"name":"Qing Lan Project of the Jiangsu Higher Education Institutions (Young and Middle-aged Academic Leader (2022)","award":["17KJB510051","KX-22-B60","2021GRFX068"],"award-info":[{"award-number":["17KJB510051","KX-22-B60","2021GRFX068"]}]},{"name":"Soft Science Research Project of Wuxi","award":["17KJB510051","KX-22-B60","2021GRFX068"],"award-info":[{"award-number":["17KJB510051","KX-22-B60","2021GRFX068"]}]},{"name":"Advanced Research and Study Project for Academic Leaders of Jiangsu Higher Vocational Colleges","award":["17KJB510051","KX-22-B60","2021GRFX068"],"award-info":[{"award-number":["17KJB510051","KX-22-B60","2021GRFX068"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>This paper investigates the formation problem of an array of large-scale mobile sensor networks. A new framework for the dynamic of mobile sensors as a continuum described by the parabolic system with boundary disturbance is proposed. The communication topology of agents is a chain graph and fixed. Leader feedback laws which are designed in a manner to the boundary control of large-scale mobile sensor networks allow the mobile sensors to achieve the formation steadily. By referring to the Lyapunov functional method and employing a boundary control approach, a new protocol is established to deal with a formation problem for the large-scale mobile sensor networks. Finally, numerical examples are given to illustrate the usefulness of the results.<\/jats:p>","DOI":"10.3390\/axioms12010009","type":"journal-article","created":{"date-parts":[[2022,12,22]],"date-time":"2022-12-22T03:24:30Z","timestamp":1671679470000},"page":"9","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["A PDE Model Approach to Formation Control of Large-Scale Mobile Sensor Networks with Boundary Uncertainties"],"prefix":"10.3390","volume":"12","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-9095-5569","authenticated-orcid":false,"given":"Xueming","family":"Qian","sequence":"first","affiliation":[{"name":"School of Internet of Things, Wuxi Vocational College of Science and Technology, Wuxi 214028, China"},{"name":"School of Internet of Things Engineering, Jiangnan University, Wuxi 214122, China"}]},{"given":"Baotong","family":"Cui","sequence":"additional","affiliation":[{"name":"School of Internet of Things Engineering, Jiangnan University, Wuxi 214122, China"}]}],"member":"1968","published-online":{"date-parts":[[2022,12,22]]},"reference":[{"key":"ref_1","first-page":"114","article-title":"A review of wireless sensor networks","volume":"4","author":"Ma","year":"2004","journal-title":"J. Commun."},{"key":"ref_2","first-page":"79","article-title":"Analysis of wireless sensor network technology and its application technology bottleneck in Internet of Things","volume":"1","author":"Xu","year":"2011","journal-title":"Internet Things Technol."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"101491","DOI":"10.1016\/j.asej.2021.05.005","article-title":"An intelligent approach for autonomous mobile robots path planning based on adaptive neuro-fuzzy inference system","volume":"13","author":"Gharajeh","year":"2022","journal-title":"Ain Shams Eng. J."},{"key":"ref_4","first-page":"731","article-title":"Swarm formation control of multiple mobile robots based agent","volume":"5","author":"Chen","year":"2006","journal-title":"Syst. Eng. Electron."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"3783","DOI":"10.1016\/j.asej.2021.04.010","article-title":"A consensus event-triggered control of networked multi-agent systems with non-ideal communication network","volume":"12","author":"Heidari","year":"2021","journal-title":"Ain Shams Eng. J."},{"key":"ref_6","first-page":"452","article-title":"Simultaneous optimization of target tracking and monitoring in mobile sensor networks","volume":"38","author":"Tu","year":"2012","journal-title":"J. Autom."},{"key":"ref_7","first-page":"202","article-title":"A consistent observation method for target tracking heterogeneous sensors in dynamic environment of mobile robots","volume":"35","author":"Wu","year":"2015","journal-title":"J. Opt."},{"key":"ref_8","first-page":"1125","article-title":"Robot trajectory tracking control based on multi-sensor fusion","volume":"27","author":"Mao","year":"2020","journal-title":"Control Eng."},{"key":"ref_9","first-page":"1413","article-title":"Application of wireless sensing technology in building environment monitoring","volume":"38","author":"Liu","year":"2011","journal-title":"Chem. Autom. Instrum."},{"key":"ref_10","first-page":"25","article-title":"A regional environmental monitoring system based on quadrotor UAVs","volume":"11","author":"Sheng","year":"2021","journal-title":"Internet Things Technol."},{"key":"ref_11","first-page":"695","article-title":"Distributed dynamic path planning algorithms in wireless sensor networks","volume":"5","author":"Jia","year":"2013","journal-title":"J. Sens. Technol."},{"key":"ref_12","first-page":"1397","article-title":"A swarming control model for mobile sensor networks based on tracking a single moving target","volume":"10","author":"Xiao","year":"2014","journal-title":"Comput. Knowl. Technol."},{"key":"ref_13","first-page":"18","article-title":"Application of cluster intelligence algorithm in WSN node localization","volume":"20","author":"Zhou","year":"2008","journal-title":"Comput. Eng."},{"key":"ref_14","first-page":"82","article-title":"Design of mobile robot system based on whisker sensor","volume":"1","author":"Fang","year":"2009","journal-title":"China Instrum."},{"key":"ref_15","first-page":"156","article-title":"Distributed target tracking based on sensing agents and movement control laws","volume":"33","author":"Wang","year":"2019","journal-title":"J. Electron. Meas. Instrum."},{"key":"ref_16","first-page":"1","article-title":"Distributed asynchronous measurement sensor network for robot control","volume":"26","author":"Zhong","year":"2011","journal-title":"Autom. Instrum."},{"key":"ref_17","first-page":"31","article-title":"Research on adaptive control of ship formation collision avoidance","volume":"39","author":"Deng","year":"2017","journal-title":"Ship Sci. Technol."},{"key":"ref_18","first-page":"1274","article-title":"Fast convergence of distributed control algorithms for arbitrary formation of robot troops","volume":"10","author":"Wang","year":"2002","journal-title":"Comput. Res. Dev."},{"key":"ref_19","first-page":"157","article-title":"UAV formation aggregation method based on differential geometry and Lie group","volume":"35","author":"Li","year":"2013","journal-title":"J. NUDT"},{"key":"ref_20","first-page":"29","article-title":"Flocking control of dynamic topology-based multiple motion agents with a leader","volume":"10","author":"Wu","year":"2008","journal-title":"J. HUST (Nat. Sci. Ed.)"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"691","DOI":"10.1038\/nphys3035","article-title":"Information transfer and behavioural inertia in starling flocks","volume":"10","author":"Attanasi","year":"2014","journal-title":"Nat. Phys."},{"key":"ref_22","first-page":"2073","article-title":"Boundary control of crowd evacuation system based on continuum model","volume":"33","author":"Qin","year":"2018","journal-title":"Control Decis."},{"key":"ref_23","first-page":"467","article-title":"Boundary control for an unstable wave equation in annular with symmetrical initial data","volume":"33","author":"Qi","year":"2016","journal-title":"J. DU (Eng. Ed.)"},{"key":"ref_24","first-page":"1356","article-title":"Boundary observation and output feedback control for spherically symmetric n-dimensional reaction diffusion equations","volume":"41","author":"Qi","year":"2015","journal-title":"J. Autom."},{"key":"ref_25","first-page":"28","article-title":"H\u221e control of delayed distributed parameter switching systems","volume":"19","author":"Bao","year":"2019","journal-title":"Sci. Technol. Eng."},{"key":"ref_26","first-page":"21","article-title":"Global synchronization in an array of coupled neural networks with impulse and time-varying delayed coupling","volume":"14","author":"Qian","year":"2011","journal-title":"J. YU (Nat. Sci. Ed.)"},{"key":"ref_27","first-page":"652","article-title":"Periodic intermittent sampling control of a class of stochastic reaction diffusion neural networks","volume":"37","author":"Luo","year":"2017","journal-title":"Syst. Sci. Math."}],"container-title":["Axioms"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2075-1680\/12\/1\/9\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T01:47:41Z","timestamp":1760147261000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2075-1680\/12\/1\/9"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,12,22]]},"references-count":27,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2023,1]]}},"alternative-id":["axioms12010009"],"URL":"https:\/\/doi.org\/10.3390\/axioms12010009","relation":{},"ISSN":["2075-1680"],"issn-type":[{"type":"electronic","value":"2075-1680"}],"subject":[],"published":{"date-parts":[[2022,12,22]]}}}