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Robust Adaptive Interval Type-2 Fuzzy Synchronization for a Class of Fractional Order Chaotic Systems

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Fractional Order Control and Synchronization of Chaotic Systems

Part of the book series: Studies in Computational Intelligence ((SCI,volume 688))

Abstract

This chapter presents a novel Robust Adaptive Interval Type-2 Fuzzy Logic Controller (RAIT2FLC) equipped with an adaptive algorithm to achieve synchronization performance for fractional order chaotic systems. In this work, by incorporating the \( H^{\infty } \) tracking design technique and Lyapunov stability criterion, a new adaptive fuzzy control algorithm is proposed so that not only the stability of the adaptive type-2 fuzzy control system is guaranteed but also the influence of the approximation error and external disturbance on the tracking error can be attenuated to an arbitrarily prescribed level via the H ∞ tracking design technique. The main contribution in this work is the use of the interval type-2 fuzzy logic controller and the numerical approximation method of Grünwald-Letnikov in order to improve the control and synchronization performance comparatively to existing results. By introducing the type-2 fuzzy control design and robustness tracking approach, the synchronization error can be attenuated to a prescribed level, even in the presence of high level uncertainties and noisy training data. A simulation example on chaos synchronization of two fractional order Duffing systems is given to verify the robustness of the proposed AIT2FLC approach in the presence of uncertainties and bounded external disturbances.

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Author information

Authors and Affiliations

  1. Department of Electrical Engineering, Mohamed Boudiaf University of M’sila, 28000, Sétif, Algeria

    Khatir Khettab

  2. Department of Electrical Engineering, Bouira University, 10000, Béjaia, Algeria

    Yassine Bensafia

  3. EEA Department, National Polytechnic School of Constantine, BP 75A RP Ali Mendjeli, 25000, Constantine, Algeria

    Samir Ladaci

Authors
  1. Khatir Khettab
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  2. Yassine Bensafia
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  3. Samir Ladaci
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Correspondence to Khatir Khettab .

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Editors and Affiliations

  1. Faculty of Computers and Information, Benha University Faculty of Computers and Information, AND Nanoelectronics Integrated Systems Center (NISC), Nile University, Egypt. , Benha, Egypt

    Ahmad Taher Azar

  2. Research and Development Centre, Vel Tech University Research and Development Centre, Chennai, Tamil Nadu, India

    Sundarapandian Vaidyanathan

  3. Department of Mathematics and CS, University of Tebessa Department of Mathematics and CS, Tebessa, Algeria

    Adel Ouannas

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Khettab, K., Bensafia, Y., Ladaci, S. (2017). Robust Adaptive Interval Type-2 Fuzzy Synchronization for a Class of Fractional Order Chaotic Systems. In: Azar, A., Vaidyanathan, S., Ouannas, A. (eds) Fractional Order Control and Synchronization of Chaotic Systems. Studies in Computational Intelligence, vol 688. Springer, Cham. https://doi.org/10.1007/978-3-319-50249-6_7

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  • DOI: https://doi.org/10.1007/978-3-319-50249-6_7

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