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.
Highlights
Dynamic chaos is a very interesting nonlinear effect which has been intensively studied during the last three decades
Since the synchronization of chaotic dynamical systems has been observed by Pecora and Carroll [2] in 1990, chaos synchronization has become a topic of great interest [3,4,5]
Different types of synchronization have been found in interacting chaotic systems, such as complete synchronization [2, 6, 7], generalized synchronization [8], phase synchronization [9], and antiphase synchronization [10]
Summary
Dynamic chaos is a very interesting nonlinear effect which has been intensively studied during the last three decades. Different types of gyros with linear/nonlinear damping are investigated for predicting the dynamic responses such as periodic and chaotic motions [17, 19, 20]. Some methods have been presented to synchronize two identical/nonidentical nonlinear gyro system such as active control [21] and neural sliding mode control [7, 8]. The goal of this paper is to synchronize two chaotic heavy symmetric gyroscope systems versus external disturbances. To achieve this goal, sliding rule-based fuzzy control is applied. Simulations are presented, to show the effectiveness of the proposed control method to chaos synchronization of chaotic gyroscope systems versus disturbances.
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