article

Discrete-time ZD, GD and NI for solving nonlinear time-varying equations

Authors:

Pei ChenAuthors Info & Claims

Numerical Algorithms, Volume 64, Issue 4

Pages 721 - 740

https://doi.org/10.1007/s11075-012-9690-7

Published: 01 December 2013 Publication History

Abstract

A special class of neural dynamics called Zhang dynamics (ZD), which is different from gradient dynamics (GD), has recently been proposed, generalized, and investigated for solving time-varying problems by following Zhang et al.'s design method. In view of potential digital hardware implemetation, discrete-time ZD (DTZD) models are proposed and investigated in this paper for solving nonlinear time-varying equations in the form of $f(x,t)=0$ . For comparative purposes, the discrete-time GD (DTGD) model and Newton iteration (NI) are also presented for solving such nonlinear time-varying equations. Numerical examples and results demonstrate the efficacy and superiority of the proposed DTZD models for solving nonlinear time-varying equations, as compared with the DTGD model and NI.

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https://dl.acm.org/doi/10.1109/TITS.2020.2983522
Yang MZhang YHu H(2021)Relationship between time-instant number and precision of ZeaD formulas with proofsNumerical Algorithms10.1007/s11075-020-01061-x88:2(883-902)Online publication date: 1-Oct-2021
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cover image Numerical Algorithms

Numerical Algorithms Volume 64, Issue 4

December 2013

161 pages

ISSN:1017-1398

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Copyright © Copyright © 2013 Springer Science+Business Media New York.

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Springer-Verlag

Berlin, Heidelberg

Publication History

Published: 01 December 2013

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Cited By

Zhang ZZhou BZheng LZhang ZSong CPei H(2021)A Varying-Parameter Adaptive Multi-Layer Neural Dynamic Method for Designing Controllers and Application to Unmanned Aerial VehiclesIEEE Transactions on Intelligent Transportation Systems10.1109/TITS.2020.298352222:8(4876-4888)Online publication date: 1-Aug-2021
https://dl.acm.org/doi/10.1109/TITS.2020.2983522
Yang MZhang YHu H(2021)Relationship between time-instant number and precision of ZeaD formulas with proofsNumerical Algorithms10.1007/s11075-020-01061-x88:2(883-902)Online publication date: 1-Oct-2021
https://dl.acm.org/doi/10.1007/s11075-020-01061-x
Huang HFu DWang GJin LLiao SWang H(2021)Modified Newton integration algorithm with noise suppression for online dynamic nonlinear optimizationNumerical Algorithms10.1007/s11075-020-00979-687:2(575-599)Online publication date: 1-Jun-2021
https://dl.acm.org/doi/10.1007/s11075-020-00979-6
Zhang YLiu XLing YYang MHuang H(2021)Continuous and discrete zeroing dynamics models using JMP function array and design formula for solving time-varying Sylvester-transpose matrix inequalityNumerical Algorithms10.1007/s11075-020-00946-186:4(1591-1614)Online publication date: 1-Apr-2021
https://dl.acm.org/doi/10.1007/s11075-020-00946-1
Luo GYang ZZhang Q(2021)Identification of autonomous nonlinear dynamical system based on discrete-time multiscale wavelet neural networkNeural Computing and Applications10.1007/s00521-021-06142-z33:22(15191-15203)Online publication date: 1-Nov-2021
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Qiu BZhang YGuo JYang ZLi X(2019)New five-step DTZD algorithm for future nonlinear minimization with quartic steady-state error patternNumerical Algorithms10.1007/s11075-018-0581-481:3(1043-1065)Online publication date: 24-Jul-2019
https://dl.acm.org/doi/10.1007/s11075-018-0581-4
Li JMao MUhlig FZhang Y(2019)A 5-instant finite difference formula to find discrete time-varying generalized matrix inverses, matrix inverses, and scalar reciprocalsNumerical Algorithms10.1007/s11075-018-0564-581:2(609-629)Online publication date: 10-Oct-2019
https://dl.acm.org/doi/10.1007/s11075-018-0564-5
Zhang YQi ZLi JQiu BYang M(2019)Stepsize domain confirmation and optimum of ZeaD formula for future optimizationNumerical Algorithms10.1007/s11075-018-0561-881:2(561-574)Online publication date: 10-Oct-2019
https://dl.acm.org/doi/10.1007/s11075-018-0561-8
Xiang QLiao BXiao LLin LLi S(2019)Discrete-time noise-tolerant Zhang neural network for dynamic matrix pseudoinversionSoft Computing - A Fusion of Foundations, Methodologies and Applications10.1007/s00500-018-3119-823:3(755-766)Online publication date: 1-Feb-2019
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Xiao L(2018)A nonlinearly activated neural dynamics and its finite-time solution to time-varying nonlinear equationNeurocomputing10.1016/j.neucom.2015.08.031173:P3(1983-1988)Online publication date: 31-Dec-2018
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