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Adaptive Synchronization of Unknown Chaotic Systems Using Mamdani Fuzzy Approach

Adaptive Synchronization of Unknown Chaotic Systems Using Mamdani Fuzzy Approach

G. El-Ghazaly
Copyright: © 2012 |Volume: 1 |Issue: 3 |Pages: 17
ISSN: 2160-9772|EISSN: 2160-9799|EISBN13: 9781466615472|DOI: 10.4018/ijsda.2012070104
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MLA

El-Ghazaly, G. "Adaptive Synchronization of Unknown Chaotic Systems Using Mamdani Fuzzy Approach." IJSDA vol.1, no.3 2012: pp.122-138. http://doi.org/10.4018/ijsda.2012070104

APA

El-Ghazaly, G. (2012). Adaptive Synchronization of Unknown Chaotic Systems Using Mamdani Fuzzy Approach. International Journal of System Dynamics Applications (IJSDA), 1(3), 122-138. http://doi.org/10.4018/ijsda.2012070104

Chicago

El-Ghazaly, G. "Adaptive Synchronization of Unknown Chaotic Systems Using Mamdani Fuzzy Approach," International Journal of System Dynamics Applications (IJSDA) 1, no.3: 122-138. http://doi.org/10.4018/ijsda.2012070104

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Abstract

The synchronization problem for a general-class of unknown chaotic systems is addressed. Fuzzy systems in Mamdani type are employed to provide an approximate model of the master chaotic system using an adaptive approach. Within this, a number of fuzzy systems are utilized to approximate the unknown nonlinear functions of the master system. An approximate model similar to the master system is constructed which is the slave system. The error dynamics between the master and slave chaotic systems is used to build a suitable control input and fuzzy systems’ parameters adaptive laws to force the slave system to be synchronized with master system. The stability of the overall synchronization system is derived based on Lyapunov stability theory. Its shown that under appropriate assumptions, the proposed approach guarantees the boundness and asymptotic convergence of synchronization errors to a small neighborhood of origin. An extensive simulation study is performed on both Duffing and Rössler chaotic systems to show the effectiveness of the proposed scheme.

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