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ISRN Artificial Intelligence
Volume 2012 (2012), Article ID 576873, 10 pages
http://dx.doi.org/10.5402/2012/576873
Research Article

Generalized Projective Synchronization of Chaotic Heavy Gyroscope Systems via Sliding Rule-Based Fuzzy Control

1Department of Mechatronics Engineering, Science and Research Branch, Islamic Azad University, Tehran, Iran
2Department of Mechatronics Engineering, Faculty of Electrical Engineering, K. N. Toosi University of Technology, Tehran, Iran
3Department of Control Engineering, Faculty of Electrical Engineering, K. N. Toosi University of Technology, Tehran, Iran

Received 5 August 2011; Accepted 17 September 2011

Academic Editor: K. Phalp

Copyright © 2012 Faezeh Farivar et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

This paper proposes the generalized projective synchronization for chaotic heavy symmetric gyroscope systems versus external disturbances via sliding rule-based fuzzy control. Because of the nonlinear terms of the gyroscope, the system exhibits complex and chaotic motions. Based on Lyapunov stability theory and fuzzy rules, the nonlinear controller and some generic sufficient conditions for global asymptotic synchronization are attained. The fuzzy rules are directly constructed subject to a common Lyapunov function such that the error dynamics of two identical chaotic motions of symmetric gyros satisfy stability in the Lyapunov sense. The proposed method allows us to arbitrarily adjust the desired scaling by controlling the slave system. It is not necessary to calculate the Lyapunov exponents and the Eigen values of the Jacobian matrix. It is a systematic procedure for synchronization of chaotic systems. It can be applied to a variety of chaotic systems no matter whether it contains external excitation or not. It needs only one controller to realize synchronization no matter how much dimensions the chaotic system contains, and the controller is easy to be implemented. The designed controller is robust versus model uncertainty and external disturbances. Numerical simulation results demonstrate the validity and feasibility of the proposed method.