{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T03:31:29Z","timestamp":1760239889096,"version":"build-2065373602"},"reference-count":56,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2019,1,10]],"date-time":"2019-01-10T00:00:00Z","timestamp":1547078400000},"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":["61572006"],"award-info":[{"award-number":["61572006"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"National Sci-Tech Support Program of China","award":["2015BAF05B03"],"award-info":[{"award-number":["2015BAF05B03"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>Wireless sensor networks (WSNs) are vulnerable to computer viruses. To protect WSNs from virus attack, the virus library associated with each sensor node must be updated in a timely way. This article is devoted to developing energy-efficient patching strategies for WSNs. First, we model the original problem as an optimal control problem in which (a) each control stands for a patching strategy, and (b) the objective functional to be optimized stands for the energy efficiency of a patching strategy. Second, we prove that the optimal control problem is solvable. Next, we derive the optimality system for solving the optimal control problem, accompanied with a few examples. Finally, we examine the effects of some factors on the optimal control. The obtained results help improve the security of WSNs.<\/jats:p>","DOI":"10.3390\/s19020262","type":"journal-article","created":{"date-parts":[[2019,1,11]],"date-time":"2019-01-11T04:10:16Z","timestamp":1547179816000},"page":"262","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":7,"title":["Energy-Efficient Patching Strategy for Wireless Sensor Networks"],"prefix":"10.3390","volume":"19","author":[{"given":"Pengdeng","family":"Li","sequence":"first","affiliation":[{"name":"School of Big Data &amp; Software Engineering, Chongqing University, Chongqing 400044, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Lu-Xing","family":"Yang","sequence":"additional","affiliation":[{"name":"School of Information Technology, Deakin University, Melbourne, VIC 3125, Australia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xiaofan","family":"Yang","sequence":"additional","affiliation":[{"name":"School of Big Data &amp; Software Engineering, Chongqing University, Chongqing 400044, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xiang","family":"Zhong","sequence":"additional","affiliation":[{"name":"School of Big Data &amp; Software Engineering, Chongqing University, Chongqing 400044, China"},{"name":"College of Mechanical and Vehicle Engineering, Hunan University, Changsha 410082, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Junhao","family":"Wen","sequence":"additional","affiliation":[{"name":"School of Big Data &amp; Software Engineering, Chongqing University, Chongqing 400044, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Qingyu","family":"Xiong","sequence":"additional","affiliation":[{"name":"School of Big Data &amp; Software Engineering, Chongqing University, Chongqing 400044, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2019,1,10]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Benhaddou, D., and Al-Fuqaha, A. 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