Fixed-time synchronization of coupled neural networks under Hölder continuous nonlinear activation function

This paper investigates the fixed-time stability of dynamical systems and its application on the fixed-time synchronization (FTSYN) of the coupled neural networks (NNs). Firstly, a new theorem on fixed-time stability is established, along with an estimation of the settling time. Based on the new the...

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Bibliographic Details
Published in:European journal of control 2025-01, Vol.81, Article 101165
Main Authors: Liu, Jing, Ren, Qifeng
Format: Article
Language:English
Subjects:
Fixed-time stability
Hölder continuous
Neural networks
Synchronization
Online Access:Get full text
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Summary:This paper investigates the fixed-time stability of dynamical systems and its application on the fixed-time synchronization (FTSYN) of the coupled neural networks (NNs). Firstly, a new theorem on fixed-time stability is established, along with an estimation of the settling time. Based on the new theorem and Lyapunov direct method, two different sufficient criteria are derived to ensure that the NNs in presence of Hölder continuity can achieve synchronization within fixed-time based on 1-norm and 2-norm, separately. Finally, two numerical simulations are conducted to demonstrate the validity and accuracy of the main findings. •A new fixed-time stability criterion of nonlinear systems is proposed.•The criterion is applied to coupled neural networks with Hölder continuous function.•The fixed-time synchronized controller is effective under both 1-norm and 2-norm.
ISSN:0947-3580
DOI:10.1016/j.ejcon.2024.101165