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Open AccessArticle

Chaotic Synchronization Using a Self-Evolving Recurrent Interval Type-2 Petri Cerebellar Model Articulation Controller

1
Faculty of Mechanical and Aerospace, Sejong University, Seoul 143-747(05006), Korea
2
Department of Electrical Electronic and Mechanical Engineering, Lac Hong University, Bien Hoa 810000, Vietnam
3
Department of Electrical Engineering, Yuan Ze University, Taoyuan 32003, Taiwan
*
Author to whom correspondence should be addressed.
This paper is an extended version of our paper published in 2019 IEEE International Conference on System Science and Engineering (ICSSE 2019), Dong Hoi, Vietnam, 20–21 July 2019; pp. 420–424.
Mathematics 2020, 8(2), 219; https://doi.org/10.3390/math8020219
Received: 2 December 2019 / Revised: 11 January 2020 / Accepted: 5 February 2020 / Published: 9 February 2020
(This article belongs to the Section Fuzzy Set Theory)
In this manuscript, the synchronization of four-dimensional (4D) chaotic systems with uncertain parameters using a self-evolving recurrent interval type-2 Petri cerebellar model articulation controller is studied. The design of the synchronization control system is comprised of a recurrent interval type-2 Petri cerebellar model articulation controller and a fuzzy compensation controller. The proposed network structure can automatically generate new rules or delete unnecessary rules based on the self-evolving algorithm. Furthermore, the gradient-descent method is applied to adjust the proposed network parameters. Through Lyapunov stability analysis, bounded system stability is guaranteed. Finally, the effectiveness of the proposed controller is illustrated using numerical simulations of 4D chaotic systems.
Keywords: chaotic systems; self-evolving algorithm; interval type-2 fuzzy system; Petri nets; cerebellar model articulation controller chaotic systems; self-evolving algorithm; interval type-2 fuzzy system; Petri nets; cerebellar model articulation controller
MDPI and ACS Style

Le, T.-L.; Huynh, T.-T.; Nguyen, V.-Q.; Lin, C.-M.; Hong, S.-K. Chaotic Synchronization Using a Self-Evolving Recurrent Interval Type-2 Petri Cerebellar Model Articulation Controller. Mathematics 2020, 8, 219.

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