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research-article

A novel adaptive active control projective synchronization of chaotic systems

[+] Author and Article Information
Boan Quan

School of Information Science and Engineering, Hunan University, Changsha 410082, China
quanboan@163.com

Chunhua Wang

School of Information Science and Engineering, Hunan University, Changsha 410082, China
wch1227164@hnu.edu.cn

Jingru Sun

School of Information Science and Engineering, Hunan University, Changsha 410082
jt_sunjr@hnu.edu.cn

Yilin Zhao

School of Information Science and Engineering, Hunan University, Changsha 410082, China
zhaoyl1992@126.com

1Corresponding author.

ASME doi:10.1115/1.4039189 History: Received May 17, 2017; Revised January 20, 2018

Abstract

This paper investigates adaptive active control projective synchronization scheme. A general synchronization controller and parameter update laws are proposed to stabilize the error system for the identical structural chaotic systems. It is the first time that the active synchronization, the projective synchronization, the adaptive synchronization are combined to achieve the synchronization of chaotic systems, which extend the control capability to achieve chaotic synchronization. By using a constant diagonal matrix, the active control is developed. Especially, when designing the controller, we just need to ensure the diagonal elements of the diagonal matrix less than or equal 0. So the synchronization of chaotic systems can be realized more easily. Furthermore, by proposing an active controller, in combination with several different control schemes, we lower the complexity of the design process of the controller. In our paper, we take Lorenz system as an example to verify the effectiveness of the proposed synchronization scheme. Theoretical analysis and numerical simulations demonstrate the feasibility of this control method.

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