Robust exponential stability of non-deterministic fuzzy neural networks: A global unidirectional quaternary implicit criterion

IF 3.4 2区数学 Q1 MATHEMATICS, APPLIED

Communications in Nonlinear Science and Numerical Simulation Pub Date : 2025-03-25 DOI:10.1016/j.cnsns.2025.108779

Wenxiao Si , Shigen Gao , Tao Wen , Ning Zhao

{"title":"Robust exponential stability of non-deterministic fuzzy neural networks: A global unidirectional quaternary implicit criterion","authors":"Wenxiao Si , Shigen Gao , Tao Wen , Ning Zhao","doi":"10.1016/j.cnsns.2025.108779","DOIUrl":null,"url":null,"abstract":"<div><div>This paper provides a sufficient criterion for robust global exponential stability (RGES) of non-deterministic fuzzy neural networks (NDFNNs), where “non-deterministic” feature maps the effect of the variability of piecewise constant argument (PCAs), derivative term coefficients (DTCs) and twofold uncertain connection weights.To determine the supremum of the non-deterministic parameters, an algorithm for the global unidirectional sequential calculation is designed, including the feasible domain of the connection weight intensities that interfere with the transient performance of NDFNNs. Furthermore, the existence and uniqueness of the solution of NDFNNs are further elucidated. These are achieved by solving quaternary implicit transcendental equations utilizing Gronwall inequality. Compared to previous results, an additional geometric representation of the allowable intensity of connection weights is provided, accounting for the influence of PCAs and DTCs, is given. The designed algorithm based on unidirectional quaternary implicit criterion fully considers the sequential relation of update process. Specifically, the unidirectional algorithm enables the supremum of subsequent elements to depend on previously computed ones, creating a coupled relationship and enhancing accuracy. Finally, the validity of the theoretical results for ensuring the RGES of NDFNNs is illustrated by the simulation cases.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"146 ","pages":"Article 108779"},"PeriodicalIF":3.4000,"publicationDate":"2025-03-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Communications in Nonlinear Science and Numerical Simulation","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S100757042500190X","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}

引用次数: 0

Abstract

This paper provides a sufficient criterion for robust global exponential stability (RGES) of non-deterministic fuzzy neural networks (NDFNNs), where “non-deterministic” feature maps the effect of the variability of piecewise constant argument (PCAs), derivative term coefficients (DTCs) and twofold uncertain connection weights.To determine the supremum of the non-deterministic parameters, an algorithm for the global unidirectional sequential calculation is designed, including the feasible domain of the connection weight intensities that interfere with the transient performance of NDFNNs. Furthermore, the existence and uniqueness of the solution of NDFNNs are further elucidated. These are achieved by solving quaternary implicit transcendental equations utilizing Gronwall inequality. Compared to previous results, an additional geometric representation of the allowable intensity of connection weights is provided, accounting for the influence of PCAs and DTCs, is given. The designed algorithm based on unidirectional quaternary implicit criterion fully considers the sequential relation of update process. Specifically, the unidirectional algorithm enables the supremum of subsequent elements to depend on previously computed ones, creating a coupled relationship and enhancing accuracy. Finally, the validity of the theoretical results for ensuring the RGES of NDFNNs is illustrated by the simulation cases.

查看原文本刊更多论文

求助全文

约1分钟内获得全文求助全文

来源期刊

Communications in Nonlinear Science and Numerical Simulation MATHEMATICS, APPLIED-MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

CiteScore

6.80

自引率

7.70%

发文量

378

审稿时长

78 days

期刊介绍： The journal publishes original research findings on experimental observation, mathematical modeling, theoretical analysis and numerical simulation, for more accurate description, better prediction or novel application, of nonlinear phenomena in science and engineering. It offers a venue for researchers to make rapid exchange of ideas and techniques in nonlinear science and complexity. The submission of manuscripts with cross-disciplinary approaches in nonlinear science and complexity is particularly encouraged. Topics of interest: Nonlinear differential or delay equations, Lie group analysis and asymptotic methods, Discontinuous systems, Fractals, Fractional calculus and dynamics, Nonlinear effects in quantum mechanics, Nonlinear stochastic processes, Experimental nonlinear science, Time-series and signal analysis, Computational methods and simulations in nonlinear science and engineering, Control of dynamical systems, Synchronization, Lyapunov analysis, High-dimensional chaos and turbulence, Chaos in Hamiltonian systems, Integrable systems and solitons, Collective behavior in many-body systems, Biological physics and networks, Nonlinear mechanical systems, Complex systems and complexity. No length limitation for contributions is set, but only concisely written manuscripts are published. Brief papers are published on the basis of Rapid Communications. Discussions of previously published papers are welcome.