Multilayer Interval Type-2 Fuzzy Controller Design for Hyperchaotic Synchronization

Abstract

This study presents a multilayer interval type-2 fuzzy controller, which applies to synchronize the hyperchaotic systems. The main contribution of this study is the design of a multilayer structure in the membership function space, which can improve the learning ability and flexibility of the type-2 fuzzy network. Using the proposed multilayer structure, the fuzzy network can reduce the number of rules while ensuring synchronization performance. Particularly, the design of 3-dimensional Gaussian membership functions (3-DGMFs) enhances the ability to against system uncertainties and external disturbances. Moreover, the structure of the proposed network can be autonomously constructed by using the self-evolving algorithm. The parameters of the proposed network are online updated using an adaptive law obtained by the gradient descent method. Finally, numerical simulations on the synchronization of hyperchaotic systems are conducted to validate the efficiency and performance of the proposed method.

Keywords

• Interval type-2 fuzzy neural network
• 3-D Gaussian membership functions
• self-evolving algorithm
• hyperchaotic systems
• adaptive control