Synchronization control for completely unknown chaotic systems via nested back-propagation neural networks

To solve the problem of existing chaotic systems with unknown nonlinearities, enormous parameters and external disturbances, in this paper, a synchronization controller with parameter adaptive laws is proposed based on nested back-propagation neural networks and the adaptive method, where the nested back-propagation neural networks are used to approximate the unknown nonlinearities based on same experiences and the unknown parameters are estimated by the adaptive method. Then the asymptotical synchronization of the drive-response chaotic systems is synthesized via state feedback controllers and updated adaptive laws. Specifically, the nested back-propagation neural networks are developed by grouping and layering the hidden neurons using the principle of partition of unity and the state domain for modularizing the concealed layer. Finally, a numerical example is given to illustrate the effectiveness of this method.