Fuzzy modeling and adaptive control of uncertain chaotic systems

A simple and systematic approach is developed for modeling and adaptive control of an unknown (or uncertain) chaotic system, using only input-output data obtained from the underlying dynamical system. Gaussian fuzzy membership functions are used in conjunction with the least-squares principle for the modeling and control. Based on the fuzzy modeling, an adaptive controller is devised, which works through self-adjusting the means and variances of the Gaussian membership functions for adaptation. The design procedure is illustrated by using the chaotic Duffing oscillator as an example, on which simulation results demonstrate the effectiveness of the proposed methodology.