Complete Synchronization and Partial Anti-Synchronization of Complex Lü Chaotic Systems by the UDE-Based Control Method

Zuoxun Wang,An Yan,Cong Song,Guijuan Wang

doi:10.3390/sym14030517

Abstract

The presence of uncertainty and disturbance can lead to asymmetric control of nonlinear systems, and this asymmetric control can lead to a decrease in the productivity of the engineered system. In order to improve the control speed of the improved nonlinear system, complete synchronization and partial anti-synchronization of complex Lü chaotic systems with uncertainty and disturbance are investigated in the present paper. First, a new UDE-based dynamic feedback control method is proposed for the complete synchronization problem of the system. The method unites the dynamic gain feedback control method and the uncertainty and perturbation estimator (UDE) control method, where the dynamic gain feedback controller is used to achieve asymptotic stability of the nominal system and the UDE controller is used to handle a given controlled system with uncertainty and disturbance. Second, for the partial desynchronization problem of this system, a new UDE-based linear-like feedback control method is proposed, which consists of two controllers: a linear-like feedback controller used to achieve the asymptotic stabilization of the nominal system and the other UDE controller is designed to handle the given controlled system with uncertainty and disturbance. Finally, numerical simulations are performed to verify the correctness and stability of the theoretical results.

Highlights

According to the experimental results, the proposed method can significantly improve the speed of the complete synchronization and partial anti-synchronization of chaotic systems and eliminate the uncertainty and disturbance of the system, which is still effective in the case of multidimensional uncertainty and disturbance
A new uncertainty and perturbation estimator (UDE)-based dynamic gain feedback control method is proposed to achieve the complete synchronization of the system, which improves the synchronization rate of the chaotic system and eliminates the uncertainty and disturbance
A new UDE-based linear-like feedback control method is proposed to achieve a partial desynchronization of the chaotic system, which enhances the anti-synchronization rate of the system and eliminates uncertainty and disturbance

Summary

Introduction

As an important branch of nonlinear systems, the control of chaotic systems has aroused substantial attention and has been widely used in secrecy communication, biological science, economics, medicine, and electric circuits and other fields. The uncertainty and disturbance in the system is unavoidable and great. How to remove uncertainties and external disturbances is directly related to the efficiency of engineering. The control of chaotic systems has been proposed from the aspects of complete synchronization, anti-synchronization, the coexistence of synchronization and anti-synchronization, partial anti-synchronization and projection synchronization, and many important results were obtained [2–10]. Among the many types of control, there is complete synchronous control, and partial anti-synchronous control, which is widely used. Partial anti-synchronous control is more demanding and difficult to implement [11–15], which causes scholars to be interested in this aspect of research, and people are bound to continue their research in relation to these two hot spots

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Methods

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Discussion

Conclusion