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Complex Noise-Resistant Zeroing Neural Network for Computing Complex Time-Dependent Lyapunov Equation

Bolin Liao Orcid Logo, Cheng Hua, Xinwei Cao, Vasilios N. Katsikis Orcid Logo, Shuai Li Orcid Logo

Mathematics, Volume: 10, Issue: 15, Start page: 2817

Swansea University Author: Shuai Li Orcid Logo

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DOI (Published version): 10.3390/math10152817

Abstract

Complex time-dependent Lyapunov equation (CTDLE), as an important means of stability analysis of control systems, has been extensively employed in mathematics and engineering application fields. Recursive neural networks (RNNs) have been reported as an effective method for solving CTDLE. In the prev...

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Published in: Mathematics
ISSN: 2227-7390
Published: MDPI AG 2022
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URI: https://cronfa.swan.ac.uk/Record/cronfa61171
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spelling 2022-10-06T14:56:40.1465582 v2 61171 2022-09-09 Complex Noise-Resistant Zeroing Neural Network for Computing Complex Time-Dependent Lyapunov Equation 42ff9eed09bcd109fbbe484a0f99a8a8 0000-0001-8316-5289 Shuai Li Shuai Li true false 2022-09-09 MECH Complex time-dependent Lyapunov equation (CTDLE), as an important means of stability analysis of control systems, has been extensively employed in mathematics and engineering application fields. Recursive neural networks (RNNs) have been reported as an effective method for solving CTDLE. In the previous work, zeroing neural networks (ZNNs) have been established to find the accurate solution of time-dependent Lyapunov equation (TDLE) in the noise-free conditions. However, noises are inevitable in the actual implementation process. In order to suppress the interference of various noises in practical applications, in this paper, a complex noise-resistant ZNN (CNRZNN) model is proposed and employed for the CTDLE solution. Additionally, the convergence and robustness of the CNRZNN model are analyzed and proved theoretically. For verification and comparison, three experiments and the existing noise-tolerant ZNN (NTZNN) model are introduced to investigate the effectiveness, convergence and robustness of the CNRZNN model. Compared with the NTZNN model, the CNRZNN model has more generality and stronger robustness. Specifically, the NTZNN model is a special form of the CNRZNN model, and the residual error of CNRZNN can converge rapidly and stably to order 10−5 when solving CTDLE under complex linear noises, which is much lower than order 10−1 of the NTZNN model. Analogously, under complex quadratic noises, the residual error of the CNRZNN model can converge to 2∥A∥F/ζ3 quickly and stably, while the residual error of the NTZNN model is divergent. Journal Article Mathematics 10 15 2817 MDPI AG 2227-7390 complex time-dependent Lyapunov equation; zeroing neural network (ZNN); complex linear noise; complex quadratic noise; noise-suppression 8 8 2022 2022-08-08 10.3390/math10152817 COLLEGE NANME Mechanical Engineering COLLEGE CODE MECH Swansea University This work was supported in part by the National Natural Science Foundation of China under Grant No. 62066015, the Natural Science Foundation of Hunan Province of China under Grant No. 2020JJ4511, and the Research Foundation of Education Bureau of Hunan Province, China, under Grant No. 20A396. 2022-10-06T14:56:40.1465582 2022-09-09T14:35:50.8238805 Faculty of Science and Engineering School of Aerospace, Civil, Electrical, General and Mechanical Engineering - Mechanical Engineering Bolin Liao 0000-0001-9036-2723 1 Cheng Hua 2 Xinwei Cao 3 Vasilios N. Katsikis 0000-0002-8208-9656 4 Shuai Li 0000-0001-8316-5289 5 61171__25335__d85f18763c6744c682a369066c4db90e.pdf 61171_VoR.pdf 2022-10-06T14:55:20.9048250 Output 1681049 application/pdf Version of Record true © 2020 by the authors. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license true eng https://creativecommons.org/licenses/by/4.0/
title Complex Noise-Resistant Zeroing Neural Network for Computing Complex Time-Dependent Lyapunov Equation
spellingShingle Complex Noise-Resistant Zeroing Neural Network for Computing Complex Time-Dependent Lyapunov Equation
Shuai Li
title_short Complex Noise-Resistant Zeroing Neural Network for Computing Complex Time-Dependent Lyapunov Equation
title_full Complex Noise-Resistant Zeroing Neural Network for Computing Complex Time-Dependent Lyapunov Equation
title_fullStr Complex Noise-Resistant Zeroing Neural Network for Computing Complex Time-Dependent Lyapunov Equation
title_full_unstemmed Complex Noise-Resistant Zeroing Neural Network for Computing Complex Time-Dependent Lyapunov Equation
title_sort Complex Noise-Resistant Zeroing Neural Network for Computing Complex Time-Dependent Lyapunov Equation
author_id_str_mv 42ff9eed09bcd109fbbe484a0f99a8a8
author_id_fullname_str_mv 42ff9eed09bcd109fbbe484a0f99a8a8_***_Shuai Li
author Shuai Li
author2 Bolin Liao
Cheng Hua
Xinwei Cao
Vasilios N. Katsikis
Shuai Li
format Journal article
container_title Mathematics
container_volume 10
container_issue 15
container_start_page 2817
publishDate 2022
institution Swansea University
issn 2227-7390
doi_str_mv 10.3390/math10152817
publisher MDPI AG
college_str Faculty of Science and Engineering
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hierarchy_top_id facultyofscienceandengineering
hierarchy_top_title Faculty of Science and Engineering
hierarchy_parent_id facultyofscienceandengineering
hierarchy_parent_title Faculty of Science and Engineering
department_str School of Aerospace, Civil, Electrical, General and Mechanical Engineering - Mechanical Engineering{{{_:::_}}}Faculty of Science and Engineering{{{_:::_}}}School of Aerospace, Civil, Electrical, General and Mechanical Engineering - Mechanical Engineering
document_store_str 1
active_str 0
description Complex time-dependent Lyapunov equation (CTDLE), as an important means of stability analysis of control systems, has been extensively employed in mathematics and engineering application fields. Recursive neural networks (RNNs) have been reported as an effective method for solving CTDLE. In the previous work, zeroing neural networks (ZNNs) have been established to find the accurate solution of time-dependent Lyapunov equation (TDLE) in the noise-free conditions. However, noises are inevitable in the actual implementation process. In order to suppress the interference of various noises in practical applications, in this paper, a complex noise-resistant ZNN (CNRZNN) model is proposed and employed for the CTDLE solution. Additionally, the convergence and robustness of the CNRZNN model are analyzed and proved theoretically. For verification and comparison, three experiments and the existing noise-tolerant ZNN (NTZNN) model are introduced to investigate the effectiveness, convergence and robustness of the CNRZNN model. Compared with the NTZNN model, the CNRZNN model has more generality and stronger robustness. Specifically, the NTZNN model is a special form of the CNRZNN model, and the residual error of CNRZNN can converge rapidly and stably to order 10−5 when solving CTDLE under complex linear noises, which is much lower than order 10−1 of the NTZNN model. Analogously, under complex quadratic noises, the residual error of the CNRZNN model can converge to 2∥A∥F/ζ3 quickly and stably, while the residual error of the NTZNN model is divergent.
published_date 2022-08-08T04:19:49Z
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score 11.012678

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