Dynamic fuzzy neural networks modeling and adaptive backstepping tracking control of uncertain chaotic systems

A simple and systematic approach is developed for modeling and neural adaptive backstepping control of an uncertain chaotic system, using only input–output data obtained from the underlying dynamical systems. Gaussian fuzzy membership functions are used in conjunction with the least-squares principle for modeling and control. Based on the dynamic fuzzy neural network (DFNN) modeling, an adaptive backstepping controller is devised, which works through structure and parameter-learning phases for adaptation. The DFNN implements Takagi–Sugeno–Kang fuzzy systems based on extended radial basis function (RBF) neural networks. The design procedure is illustrated by using the multiscroll chaotic attractors as an example, on which simulation results demonstrate the effectiveness of the proposed methodology.