Wavelet Interval Type-2 Fuzzy Quad-Function-Link Brain Emotional Control Algorithm for the Synchronization of 3D Nonlinear Chaotic Systems

This study provides a novel quad-function-link network to adjust the lower and upper weights of a wavelet interval type-2 fuzzy brain emotional structure to increase the response and performance for the synchronization of 3D nonlinear chaotic systems. The proposed control system is a hybrid method that comprises a new wavelet interval type-2 fuzzy quad-function-link brain emotional controller and a robust controller. It contains a fuzzy inference system and three substructures with five layers. The substructures are an amygdala, a prefrontal cortex, and a novel quad-function-link network that can adjust the weights efficiently for the amygdala and prefrontal cortex networks to achieve the synchronization of the master–slave systems well with reduced tracking errors. Then, a Lyapunov stability function is employed to provide the adaptive laws, and they are effectively used online to adjust the system parameters. Finally, simulation studies of two 3D nonlinear chaotic systems are used to verify the superiority and advantage of the proposed algorithm.