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Improved ZND model for solving dynamic linear complex matrix equation and its application

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Abstract

The online solving of a dynamic linear complex matrix equation (DLCME) is commonly encountered in many fields, and it exists for lots of engineering applications. For solving the DLCME, the gradient neural dynamics (GND) and the zeroing neural dynamics (ZND) are usually designed based on a predefined error function in scalar or matrix form to monitor the residual error convergence, respectively. In this paper, in order to improve the adaptability as the residual error decreasing with time and to release the limitation of convex activation function, an improved zeroing neural dynamics (IZND) model is proposed with a residual-based adaptive coefficient and a non-convex activation function. By using the Lyapunov stability theory, the global convergence and noise suppression of the proposed IZND model are theoretically discussed under the noise-free and noise-perturbed circumstances. Then, simulative verifications and a dynamic acoustic source localization application illustrate the efficacy and superiority of the proposed model for solving the DLCME. Comparing with some existing GND and ZND models, the proposed IZND model shows advanced performance in solution accuracy, noise suppression and convergence rate.

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Acknowledgements

This work is supported in part by the Natural Science Foundation of Guangdong Province, China (No. 2021A1515011847), in part by Postgraduate Education Innovation Project of Guangdong Ocean University (No. 202214, 202250, 202251, 202160), in part by the Special Project in Key Fields of Universities in Department of Education of Guangdong Province (No. 2019KZDZX1036), in part by the Key Lab of Digital Signal and Image Processing of Guangdong Province (No. 2019GDDSIPL-01).

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  1. College of Electronic and Information Engineering, Guangdong Ocean University, Zhanjiang, 524088, China

    Zhiyuan Song, Zhenyao Lu, Jiahao Wu, Xiuchun Xiao & Guancheng Wang

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Correspondence to Xiuchun Xiao.

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We wish to draw the attention of the Editor to the following facts, which may be considered as potential conflicts of interest and to significant financial contributions to this work. We confirm that the manuscript has been read and approved by all named authors and that there are no other persons who satisfied the criteria for authorship but are not listed. We further confirm that the other of authors listed in the manuscript has been approved by all of us and that the second author prepared the revision information letter and addressed most of the comments. We confirm that we have given due consideration to the protection of intellectual property associated with this work and that there are no impediments to publication, including the timing of publication, with respect to intellectual property. In so doing we confirm that we have followed the regulations of our institutions concerning intellectual property. We understand that the Corresponding Author is the sole contact for the Editorial process (including Editorial Manager and direct communications with the office ). He is responsible for communicating with the other authors about progress, submissions of revision and final approval of proof. We confirm that we have provided a current email address, which is accessible by the corresponding author, which has been configured to accept email from the Neural Computing and Applications Editorial Office.

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Song, Z., Lu, Z., Wu, J. et al. Improved ZND model for solving dynamic linear complex matrix equation and its application. Neural Comput & Applic 34, 21035–21048 (2022). https://doi.org/10.1007/s00521-022-07581-y

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