Adaptive gain fuzzy sliding mode control for the synchronization of nonlinear chaotic gyros

This paper proposes an adaptive gain fuzzy sliding mode control (AGFSMC) scheme for the synchronization of two nonlinear chaotic gyros in the presence of model uncertainties and external disturbances. In the AGFSMC scheme, the hitting controller that drives the system to the sliding surface is constructed by a set of fuzzy rules. In the proposed method, the gain of the reaching controller is adaptively adjusted to provide robustness against bounded uncertainties and external disturbances. The AGFSMC scheme can provide robustness in the absence of any knowledge about the bounds of uncertainties and external disturbances. We show that the adaptive gain scheme used in AGFSMC, improves the performance in comparison with the same control methodology that uses a fixed gain. Theoretical analysis of the AGFSMC scheme based on Lyapunov stability theory is provided. Numerical simulation on the application of the proposed method for the synchronization of two chaotic gyros is provided to demonstrate the feasibility of the method.