Zeroing Neural Network Approaches Based on Direct and Indirect Methods for Solving the Yang–Baxter-like Matrix Equation

This research introduces three novel zeroing neural network (ZNN) models for addressing the time-varying Yang–Baxter-like matrix equation (TV-YBLME) with arbitrary (regular or singular) real time-varying (TV) input matrices in continuous time. One ZNN dynamic utilizes error matrices directly arising...

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Bibliographic Details
Published in:Mathematics (Basel) 2022-06, Vol.10 (11), p.1950
Main Authors: Jiang, Wendong, Lin, Chia-Liang, Katsikis, Vasilios N., Mourtas, Spyridon D., Stanimirović, Predrag S., Simos, Theodore E.
Format: Article
Language:English
Subjects:
dynamical system
Dynamical systems
Food science
Mathematical research
Matrices
Methods
Neural networks
Numerical analysis
Regularization
Tikhonov regularization
Yang–Baxter-like matrix equation (YBLME)
zeroing neural network (ZNN)
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Summary:This research introduces three novel zeroing neural network (ZNN) models for addressing the time-varying Yang–Baxter-like matrix equation (TV-YBLME) with arbitrary (regular or singular) real time-varying (TV) input matrices in continuous time. One ZNN dynamic utilizes error matrices directly arising from the equation involved in the TV-YBLME. Moreover, two ZNN models are proposed using basic properties of the YBLME, such as the splitting of the YBLME and sufficient conditions for a matrix to solve the YBLME. The Tikhonov regularization principle enables addressing the TV-YBLME with an arbitrary input real TV matrix. Numerical experiments, including nonsingular and singular TV input matrices, show that the suggested models deal effectively with the TV-YBLME.
ISSN:2227-7390
2227-7390
DOI:10.3390/math10111950