Fuzzy Adaptive Control of a Fractional Order Chaotic System With Unknown Control Gain Sign Using a Fractional Order Nussbaum Gain |
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| Authors: | Khatir Khettab Samir Ladaci Yassine Bensafia |
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| Affiliation: | 1.Electrical Engineering Department, University of Mohamed Boudiaf, M'sila 28000, Algeria2.Electrical Engineering Department, University of Skikda, Skikda 21000, Algeria3.EEA Department, National Polytechnic School of Constantine, B. P. 75 A, Ali Mendjli 25000 Constantine, Algeria4.SP-Lab Laboratory, Department of Electronics, Mentouri University, Route de Ain Elbey, Constantine 25000, Algeria5.Electrical Engineering Department, University of Bouira, 10000 Bouira, Algeria |
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| Abstract: | 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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| Keywords: | Adaptive fuzzy control chaos synchronization fractional order Nussbaum function Lyapunov stability nonlinear fractional order systems |
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