{"title":"Fixed-time synchronization of coupled neural networks under Hölder continuous nonlinear activation function","authors":"Jing Liu, Qifeng Ren","doi":"10.1016/j.ejcon.2024.101165","DOIUrl":null,"url":null,"abstract":"<div><div>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.</div></div>","PeriodicalId":50489,"journal":{"name":"European Journal of Control","volume":"81 ","pages":"Article 101165"},"PeriodicalIF":2.5000,"publicationDate":"2025-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"European Journal of Control","FirstCategoryId":"94","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0947358024002255","RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"AUTOMATION & CONTROL SYSTEMS","Score":null,"Total":0}
引用次数: 0
Abstract
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.
期刊介绍：
The European Control Association (EUCA) has among its objectives to promote the development of the discipline. Apart from the European Control Conferences, the European Journal of Control is the Association''s main channel for the dissemination of important contributions in the field.
The aim of the Journal is to publish high quality papers on the theory and practice of control and systems engineering.
The scope of the Journal will be wide and cover all aspects of the discipline including methodologies, techniques and applications.
Research in control and systems engineering is necessary to develop new concepts and tools which enhance our understanding and improve our ability to design and implement high performance control systems. Submitted papers should stress the practical motivations and relevance of their results.
The design and implementation of a successful control system requires the use of a range of techniques:
Modelling
Robustness Analysis
Identification
Optimization
Control Law Design
Numerical analysis
Fault Detection, and so on.
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