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.
Highlights
The concept of fuzzy sets, known as type-1 fuzzy systems (T1FSs), was proposed by Zadeh in 1965 [1]
Based on the above discussions, this study presents a self-evolving multilayer interval type-2 fuzzy controller (SMIT2FC) to enhance the synchronization performance of the hyperchaotic synchronization system
The procedure of online self-evolving algorithm is given as follow: Step 1: Initialize the structure of the SMIT2FC network with a few membership functions and initial corresponding rules
Summary
The concept of fuzzy sets, known as type-1 fuzzy systems (T1FSs), was proposed by Zadeh in 1965 [1]. In 2021, Singh et al provided a multiswitching synchronization of nonlinear hyperchaotic systems via backstepping control [51] Most of their methods are complex, and the performance can be further improved. Based on the above discussions, this study presents a self-evolving multilayer interval type-2 fuzzy controller (SMIT2FC) to enhance the synchronization performance of the hyperchaotic synchronization system. The main contributions of this study can be list as follow: (1) The design of multilayer structure to improve the learning ability and flexibility of the interval type-2 fuzzy network; (2) The design of the selfevolving algorithm can help the network automatically construct its structure with suitable membership functions and rules; (3) The 3-DGMFs are used to better scope with system uncertainties and external disturbances.
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