A new fixed-time stability theorem and its application to the fixed-time synchronization of neural networks

Chuan Chen; Lixiang Li; Haipeng Peng; Yixian Yang; Ling Mi; Hui Zhao

doi:10.1016/j.neunet.2019.12.028

A new fixed-time stability theorem and its application to the fixed-time synchronization of neural networks

Neural Netw. 2020 Mar:123:412-419. doi: 10.1016/j.neunet.2019.12.028. Epub 2020 Jan 7.

Authors

Chuan Chen¹, Lixiang Li², Haipeng Peng³, Yixian Yang⁴, Ling Mi⁵, Hui Zhao⁶

Affiliations

¹ School of Cyber Security, Qilu University of Technology, Jinan 250353, China; Shandong Provincial Key Laboratory of Computer Networks, Jinan, 250353, China. Electronic address: chenchuan2019@qlu.edu.cn.
² Information Security Center, State Key Laboratory of Networking and Switching Technology, Beijing University of Posts and Telecommunications, Beijing 100876, China. Electronic address: lixiang@bupt.edu.cn.
³ Information Security Center, State Key Laboratory of Networking and Switching Technology, Beijing University of Posts and Telecommunications, Beijing 100876, China. Electronic address: penghaipeng@bupt.edu.cn.
⁴ Information Security Center, State Key Laboratory of Networking and Switching Technology, Beijing University of Posts and Telecommunications, Beijing 100876, China. Electronic address: yxyang@bupt.edu.cn.
⁵ School of Mathematics and Statistics, Qilu University of Technology, Jinan 250353, China. Electronic address: miling@lyu.edu.cn.
⁶ School of Information Science and Engineering, University of Jinan, Jinan 250022, China. Electronic address: ise_zhaohui@ujn.edu.cn.

PMID: 31945620
DOI: 10.1016/j.neunet.2019.12.028

Abstract

In this paper, we derive a new fixed-time stability theorem based on definite integral, variable substitution and some inequality techniques. The fixed-time stability criterion and the upper bound estimate formula for the settling time are different from those in the existing fixed-time stability theorems. Based on the new fixed-time stability theorem, the fixed-time synchronization of neural networks is investigated by designing feedback controller, and sufficient conditions are derived to guarantee the fixed-time synchronization of neural networks. To show the usability and superiority of the obtained theoretical results, we propose a secure communication scheme based on the fixed-time synchronization of neural networks. Numerical simulations illustrate that the new upper bound estimate formula for the settling time is much tighter than those in the existing fixed-time stability theorems. Moreover, the plaintext signals can be recovered according to the new fixed-time stability theorem, while the plaintext signals cannot be recovered according to the existing fixed-time stability theorems.

Keywords: Fixed-time stability; Fixed-time synchronization; Neural networks.

MeSH terms

Feedback
Neural Networks, Computer*
Time Factors