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Journal of Control Science and Engineering
Volume 2017, Article ID 9562818, 11 pages
https://doi.org/10.1155/2017/9562818
Research Article

Synchronization of Two Fractional-Order Chaotic Systems via Nonsingular Terminal Fuzzy Sliding Mode Control

1School of Information Engineering, Henan University of Science and Technology, Luoyang 471023, China
2Industrial Engineering School, University of Extremadura, Badajoz, Spain
3School of Electrical Engineering, Henan University of Science and Technology, Luoyang 471023, China

Correspondence should be addressed to Xiaona Song; moc.361@79_anoaix

Received 23 February 2017; Accepted 6 July 2017; Published 17 August 2017

Academic Editor: Petko Petkov

Copyright © 2017 Xiaona Song et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

The synchronization of two fractional-order complex chaotic systems is discussed in this paper. The parameter uncertainty and external disturbance are included in the system model, and the synchronization of the considered chaotic systems is implemented based on the finite-time concept. First, a novel fractional-order nonsingular terminal sliding surface which is suitable for the considered fractional-order systems is proposed. It is proven that once the state trajectories of the system reach the proposed sliding surface they will converge to the origin within a given finite time. Second, in terms of the established nonsingular terminal sliding surface, combining the fuzzy control and the sliding mode control schemes, a novel robust single fuzzy sliding mode control law is introduced, which can force the closed-loop dynamic error system trajectories to reach the sliding surface over a finite time. Finally, using the fractional Lyapunov stability theorem, the stability of the proposed method is proven. The proposed method is implemented for synchronization of two fractional-order Genesio-Tesi chaotic systems with uncertain parameters and external disturbances to verify the effectiveness of the proposed fractional-order nonsingular terminal fuzzy sliding mode controller.