{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,5]],"date-time":"2026-08-05T04:50:11Z","timestamp":1785905411527,"version":"3.56.0"},"reference-count":34,"publisher":"MDPI AG","issue":"8","license":[{"start":{"date-parts":[[2026,8,1]],"date-time":"2026-08-01T00:00:00Z","timestamp":1785542400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>This work investigates the adaptive event-triggered distributed estimation problem for discrete time-varying nonlinear stochastic systems over sensor networks exposed to replay attacks within a finite-horizon setting. The sensor network comprises multiple nodes whose interaction structure is described by two randomly switching directed graphs. The plant under consideration is formulated as a discrete time-varying nonlinear stochastic system obeying a sector-bounded condition. To mitigate communication overhead, an adaptive event-triggered scheme is employed, where the triggering threshold is dynamically updated based on the triggering error. In addition, replay attacks are considered, wherein an adversary randomly replaces current data packets with previously recorded ones. A compensation mechanism is devised to neutralize the impact of such attacks. By building a distributed estimator and formulating an augmented estimation error system, sufficient criteria are established via Lyapunov theory and stochastic analysis to ensure the prescribed average H\u221e performance level is attained. The estimator gains are computed recursively by solving a sequence of recursive linear matrix inequalities (RLMIs). A design algorithm for the distributed estimator is also provided to support online implementation. Finally, a numerical simulation example is given to demonstrate the effectiveness of the proposed estimation approach.<\/jats:p>","DOI":"10.3390\/e28080859","type":"journal-article","created":{"date-parts":[[2026,8,3]],"date-time":"2026-08-03T15:51:23Z","timestamp":1785772283000},"page":"859","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Adaptive Event-Triggered Distributed Estimation for a Class of Non-Linear Systems over Sensor Networks with Replay Attacks: The Finite-Horizon Case"],"prefix":"10.3390","volume":"28","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-4094-8915","authenticated-orcid":false,"given":"Xianye","family":"Bu","sequence":"first","affiliation":[{"name":"School of Electrical and Information Engineering, Northeast Petroleum University, Daqing 163318, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Tao","family":"Lu","sequence":"additional","affiliation":[{"name":"School of Electrical and Information Engineering, Northeast Petroleum University, Daqing 163318, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Wenbo","family":"Dong","sequence":"additional","affiliation":[{"name":"School of Electrical and Information Engineering, Northeast Petroleum University, Daqing 163318, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jiahui","family":"Li","sequence":"additional","affiliation":[{"name":"Artificial Intelligence Energy Research Institute, Northeast Petroleum University, Daqing 163318, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3827-2357","authenticated-orcid":false,"given":"Nan","family":"Hou","sequence":"additional","affiliation":[{"name":"Artificial Intelligence Energy Research Institute, Northeast Petroleum University, Daqing 163318, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2026,8,1]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"662","DOI":"10.1080\/03081079.2015.1106733","article-title":"Distributed fault estimation with randomly occurring uncertainties over sensor networks","volume":"45","author":"Dong","year":"2016","journal-title":"Int. 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