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Volume 6 Issue 3
May  2019

IEEE/CAA Journal of Automatica Sinica

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Article Contents
Khatir Khettab, Samir Ladaci and Yassine Bensafia, "Fuzzy Adaptive Control of a Fractional Order Chaotic System With Unknown Control Gain Sign Using a Fractional Order Nussbaum Gain," IEEE/CAA J. Autom. Sinica, vol. 6, no. 3, pp. 816-823, May 2019. doi: 10.1109/JAS.2016.7510169
 Citation: Khatir Khettab, Samir Ladaci and Yassine Bensafia, "Fuzzy Adaptive Control of a Fractional Order Chaotic System With Unknown Control Gain Sign Using a Fractional Order Nussbaum Gain," IEEE/CAA J. Autom. Sinica, vol. 6, no. 3, pp. 816-823, May 2019.

# Fuzzy Adaptive Control of a Fractional Order Chaotic System With Unknown Control Gain Sign Using a Fractional Order Nussbaum Gain

##### doi: 10.1109/JAS.2016.7510169
Funds:

the Algerian Ministry of Higher Education and Scientific Research (MESRS) for CNEPRU Research Project A01L08UN210120110001

• In this paper we propose an improved fuzzy adaptive control strategy, for a class of nonlinear chaotic fractional order (SISO) systems with unknown control gain sign. The online control algorithm uses fuzzy logic sets for the identification of the fractional order chaotic system, whereas the lack of a priori knowledge on the control directions is solved by introducing a fractional order Nussbaum gain. Based on Lyapunov stability theorem, stability analysis is performed for the proposed control method for an acceptable synchronization error level. In this work, the Grünwald-Letnikov method is used for numerical approximation of the fractional order systems. A simulation example is given to illustrate the effectiveness of the proposed control scheme.

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