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The proposed novel control law attenuates the chattering phenomena of the conventional sliding mode controller. In addition, a non-singular fast terminal sliding mode surface is employed to remove the singularity problem, increase the convergence rate, and guarantee finite-time convergence. An extreme learning machine (ELM) neural network is utilized to estimate the unknown dynamics of the spur gear system and the reaching law coefficients; hence, this control scheme is a combination of the direct and indirect adaptive control. The adaptation rules of the ELM are derived based on the Lyapunov stability theorem to ensure closed-looped stability. Finally, some different numerical simulations are considered to check the validity and efficiency of the proposed control strategy compared with other control methods.<\/jats:p>","DOI":"10.1177\/01423312221087578","type":"journal-article","created":{"date-parts":[[2022,5,2]],"date-time":"2022-05-02T04:03:47Z","timestamp":1651464227000},"page":"2795-2808","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":8,"title":["Control and synchronization of chaotic spur gear system using adaptive non-singular fast terminal sliding mode controller"],"prefix":"10.1177","volume":"44","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-9124-4139","authenticated-orcid":false,"given":"Mohammad Ali","family":"Labbaf Khaniki","sequence":"first","affiliation":[{"name":"Faculty of Electrical Engineering, K.N. 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