Nonlinear rule-based controller for chaos synchronization of two gyros with linear-plus-cubic damping

In this paper we show how the chaotic behavior of two nonlinear gyros can be synchronized via fuzzy logic controller. Based on Lyapunov stability theory and fuzzy rules, the nonlinear controller and some generic sufficient conditions for global asymptotic synchronization are attained. We directly construct the fuzzy rules 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. It overcomes the trial-and-error tuning for the membership functions and rule base in traditional fuzzy logic control (FLC). Numerical simulation results demonstrate the validity and feasibility of the proposed controller.