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Algorithms 2018, 11(7), 101; https://doi.org/10.3390/a11070101

Robust Fuzzy Adaptive Sliding Mode Stabilization for Fractional-Order Chaos

1
Department of Electrical Engineering, Sétif 1 University, Sétif 19000, Algeria
2
Department of Electronics, Electrotechnics and Automatics (EEA), Office 447, BP 75 A, National Polytechnic School of Constantine, Nouvelle ville Ali Mendjli, Constantine 25100, Algeria
3
Laboratory of Signal Processing (SP-Lab), Department of Electronics, University of Mentouri Brothers Constantine 1, Route de Ain Elbey, Constantine 25000, Algeria
*
Author to whom correspondence should be addressed.
Received: 1 June 2018 / Revised: 3 July 2018 / Accepted: 5 July 2018 / Published: 7 July 2018
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Abstract

In this paper, a new adaptive fuzzy sliding mode control (AFSMC) design strategy is proposed for the control of a special class of three-dimensional fractional order chaotic systems with uncertainties and external disturbance. The design methodology is developed in two stages: first, an adaptive sliding mode control law is proposed for the class of fractional order chaotic systems without uncertainties, and then a fuzzy logic system is used to estimate the control compensation effort to be added in the case of uncertainties on the system’s model. Based on the Lyapunov theory, the stability analysis of both control laws is provided with elimination of the chattering action in the control signal. The developed control scheme is simple to implement and the overall control scheme guarantees the global asymptotic stability in the Lyapunov sense if all the involved signals are uniformly bounded. In the present work, simulation studies on fractional-order Chen chaotic systems are carried out to show the efficiency of the proposed fractional adaptive controllers. View Full-Text
Keywords: chaotic systems; fractional-order system; sliding mode control; adaptive fuzzy control; Lyapunov stability chaotic systems; fractional-order system; sliding mode control; adaptive fuzzy control; Lyapunov stability
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Bourouba, B.; Ladaci, S. Robust Fuzzy Adaptive Sliding Mode Stabilization for Fractional-Order Chaos. Algorithms 2018, 11, 101.

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