Fuzzy Adaptive Sliding Mode Control of Chaos

Abstract

A simple and systematic approach is developed for modeling and adaptive control of an unknown (or uncertain) chaotic system of the formx(n) = f(X) + g(X)u, using only input-output data obtained from the underlying dynamic system. Two different fuzzy identification methods, i.e. least-squares and gradient descent, are used for identifying the unknown functions f(X) and g(X). Based on the fuzzy modeling, an adaptive controller is devised, which works through sliding mode method. The presented procedure is illustrated by using the chaotic system-modified Duffing's equation as an example, on which simulation results demonstrate the effectiveness of the proposed adaptive algorithm.