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An Adaptive Interval Type-2 Fuzzy Sliding Mode Control Scheme for Fractional Chaotic Systems Synchronization With Chattering Elimination: Fractional Adaptive PI-Regulator Approach

An Adaptive Interval Type-2 Fuzzy Sliding Mode Control Scheme for Fractional Chaotic Systems Synchronization With Chattering Elimination: Fractional Adaptive PI-Regulator Approach

Khatir Khettab, Yassine Bensafia
Copyright: © 2018 |Pages: 30
ISBN13: 9781522554189|ISBN10: 1522554181|EISBN13: 9781522554196
DOI: 10.4018/978-1-5225-5418-9.ch004
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MLA

Khettab, Khatir, and Yassine Bensafia. "An Adaptive Interval Type-2 Fuzzy Sliding Mode Control Scheme for Fractional Chaotic Systems Synchronization With Chattering Elimination: Fractional Adaptive PI-Regulator Approach." Advanced Synchronization Control and Bifurcation of Chaotic Fractional-Order Systems, edited by Abdesselem Boulkroune and Samir Ladaci, IGI Global, 2018, pp. 99-128. https://doi.org/10.4018/978-1-5225-5418-9.ch004

APA

Khettab, K. & Bensafia, Y. (2018). An Adaptive Interval Type-2 Fuzzy Sliding Mode Control Scheme for Fractional Chaotic Systems Synchronization With Chattering Elimination: Fractional Adaptive PI-Regulator Approach. In A. Boulkroune & S. Ladaci (Eds.), Advanced Synchronization Control and Bifurcation of Chaotic Fractional-Order Systems (pp. 99-128). IGI Global. https://doi.org/10.4018/978-1-5225-5418-9.ch004

Chicago

Khettab, Khatir, and Yassine Bensafia. "An Adaptive Interval Type-2 Fuzzy Sliding Mode Control Scheme for Fractional Chaotic Systems Synchronization With Chattering Elimination: Fractional Adaptive PI-Regulator Approach." In Advanced Synchronization Control and Bifurcation of Chaotic Fractional-Order Systems, edited by Abdesselem Boulkroune and Samir Ladaci, 99-128. Hershey, PA: IGI Global, 2018. https://doi.org/10.4018/978-1-5225-5418-9.ch004

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Abstract

This chapter presents a fractional adaptive interval type-2 fuzzy logic control strategy based on active fractional sliding mode controller (FAIT2FSMC) to synchronize tow chaotic fractional-order systems. The interval type-2 fuzzy logic systems (IT2FLS) are used to approximate the plant dynamics represented by unknown functions of the system, and the IT2F adaptation law adjusts the consequent parameters of the rules based on a Lyapunov synthesis approach. One of the main contributions in this work is the use of an IT2F and an adaptive fractional order PIλ control law to eliminate the chattering action in the control signal. Based on fractional order Lyapunov stability criterion, stability analysis is performed for the proposed method for an acceptable synchronization error level. The performance of the proposed scheme is demonstrated through the synchronization of two different fractional order chaotic gyro systems. Simulations are implemented using a numerical method based on Grünwald-Letnikov approach to solve the fractional differential equations.

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