Next Article in Journal
Advanced Artificial Neural Networks
Next Article in Special Issue
Solutions to the Sub-Optimality and Stability Issues of Recursive Pole and Zero Distribution Algorithms for the Approximation of Fractional Order Models
Previous Article in Journal
A Self-Adaptive Evolutionary Algorithm for the Berth Scheduling Problem: Towards Efficient Parameter Control
Previous Article in Special Issue
Experimental Validation of a Novel Auto-Tuning Method for a Fractional Order PI Controller on an UR10 Robot
Open AccessArticle

Robust Fuzzy Adaptive Sliding Mode Stabilization for Fractional-Order Chaos

Department of Electrical Engineering, Sétif 1 University, Sétif 19000, Algeria
Department of Electronics, Electrotechnics and Automatics (EEA), Office 447, BP 75 A, National Polytechnic School of Constantine, Nouvelle ville Ali Mendjli, Constantine 25100, Algeria
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.
Algorithms 2018, 11(7), 101;
Received: 1 June 2018 / Revised: 3 July 2018 / Accepted: 5 July 2018 / Published: 7 July 2018
PDF [1827 KB, uploaded 7 July 2018]


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

Figure 1

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 (CC BY 4.0).

Share & Cite This Article

MDPI and ACS Style

Bourouba, B.; Ladaci, S. Robust Fuzzy Adaptive Sliding Mode Stabilization for Fractional-Order Chaos. Algorithms 2018, 11, 101.

Show more citation formats Show less citations formats

Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.

Related Articles

Article Metrics

Article Access Statistics



[Return to top]
Algorithms EISSN 1999-4893 Published by MDPI AG, Basel, Switzerland RSS E-Mail Table of Contents Alert
Back to Top