FLS-based adaptive control for a class of chaotic systems

A FLS-based adaptive control approach with stability analysis is proposed to control a class of chaotic system with unknown nonlinear function to track a reference trajectory. Fuzzy logic system (FLS) is introduced to parameterize the unknown nonlinear function; an n-dimension supervisory controller attaching to the adaptive controller is developed to guarantee the boundedness of the output signal. It is proved that 1) the closed-loop system using this FLS-based adaptive controller is globally stable in the sense that all signals involved are bounded and 2) the tracking error converges to zero asymptotically if the minimum approximation error between the optimal approximation of unknown nonlinear function and the true function is squared integrable. Finally, we apply this adaptive controller to control the Duffing oscillator to track a period orbit; the simulation results show the validity.