Mathematical Problems in Engineering
Volume 2011 (2011), Article ID 701671, 20 pages
Research Article

Chaos Synchronization Using Adaptive Dynamic Neural Network Controller with Variable Learning Rates

1Department of Electrical Engineering, National Chung-Hsing University, Taichung 402, Taiwan
2Department of Electrical Engineering, Chung Hua University, Hsinchu 300, Taiwan

Received 22 July 2010; Accepted 20 January 2011

Academic Editor: E. E. N. Macau

Copyright © 2011 Chih-Hong Kao et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


This paper addresses the synchronization of chaotic gyros with unknown parameters and external disturbance via an adaptive dynamic neural network control (ADNNC) system. The proposed ADNNC system is composed of a neural controller and a smooth compensator. The neural controller uses a dynamic RBF (DRBF) network to online approximate an ideal controller. The DRBF network can create new hidden neurons online if the input data falls outside the hidden layer and prune the insignificant hidden neurons online if the hidden neuron is inappropriate. The smooth compensator is designed to compensate for the approximation error between the neural controller and the ideal controller. Moreover, the variable learning rates of the parameter adaptation laws are derived based on a discrete-type Lyapunov function to speed up the convergence rate of the tracking error. Finally, the simulation results which verified the chaotic behavior of two nonlinear identical chaotic gyros can be synchronized using the proposed ADNNC scheme.