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A Novel Zeroing Neural Network for Solving Time-Varying Quadratic Matrix Equations against Linear Noises

Jianfeng Li, Linxi Qu, Zhan Li, Bolin Liao, Shuai Li Orcid Logo, Yang Rong Orcid Logo, Zheyu Liu, Zhijie Liu, Kunhuang Lin

Mathematics, Volume: 11, Issue: 2, Start page: 475

Swansea University Authors: Zhan Li, Shuai Li Orcid Logo

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DOI (Published version): 10.3390/math11020475

Abstract

The solving of quadratic matrix equations is a fundamental issue which essentially exists in the optimal control domain. However, noises exerted on the coefficients of quadratic matrix equations may affect the accuracy of the solutions. In order to solve the time-varying quadratic matrix equation pr...

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Published in: Mathematics
ISSN: 2227-7390
Published: MDPI AG 2023
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URI: https://cronfa.swan.ac.uk/Record/cronfa62487
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However, noises exerted on the coefficients of quadratic matrix equations may affect the accuracy of the solutions. In order to solve the time-varying quadratic matrix equation problem under linear noise, a new error-processing design formula is proposed, and a resultant novel zeroing neural network model is developed. The new design formula incorporates a second-order error-processing manner, and the double-integration-enhanced zeroing neural network (DIEZNN) model is further proposed for solving time-varying quadratic matrix equations subject to linear noises. Compared with the original zeroing neural network (OZNN) model, finite-time zeroing neural network (FTZNN) model and integration-enhanced zeroing neural network (IEZNN) model, the DIEZNN model shows the superiority of its solution under linear noise; that is, when solving the problem of a time-varying quadratic matrix equation in the environment of linear noise, the residual error of the existing model will maintain a large level due to the influence of linear noise, which will eventually lead to the solution&#x2019;s failure. The newly proposed DIEZNN model can guarantee a normal solution to the time-varying quadratic matrix equation task no matter how much linear noise there is. In addition, the theoretical analysis proves that the neural state of the DIEZNN model can converge to the theoretical solution even under linear noise. The computer simulation results further substantiate the superiority of the DIEZNN model in solving time-varying quadratic matrix equations under linear noise.</abstract><type>Journal Article</type><journal>Mathematics</journal><volume>11</volume><journalNumber>2</journalNumber><paginationStart>475</paginationStart><paginationEnd/><publisher>MDPI AG</publisher><placeOfPublication/><isbnPrint/><isbnElectronic/><issnPrint/><issnElectronic>2227-7390</issnElectronic><keywords>time-varying quadratic matrix equation; double-integration-enhanced zeroing neural network; linear noise</keywords><publishedDay>16</publishedDay><publishedMonth>1</publishedMonth><publishedYear>2023</publishedYear><publishedDate>2023-01-16</publishedDate><doi>10.3390/math11020475</doi><url/><notes/><college>COLLEGE NANME</college><department>Computer Science</department><CollegeCode>COLLEGE CODE</CollegeCode><DepartmentCode>SCS</DepartmentCode><institution>Swansea University</institution><apcterm/><funders>This study was supported in part by the National Natural Science Foundation of China (61962023 and 62066015)</funders><projectreference/><lastEdited>2023-03-02T14:33:30.8271616</lastEdited><Created>2023-02-03T11:38:55.4475639</Created><path><level id="1">Faculty of Science and Engineering</level><level id="2">School of Mathematics and Computer Science - Computer Science</level></path><authors><author><firstname>Jianfeng</firstname><surname>Li</surname><order>1</order></author><author><firstname>Linxi</firstname><surname>Qu</surname><order>2</order></author><author><firstname>Zhan</firstname><surname>Li</surname><order>3</order></author><author><firstname>Bolin</firstname><surname>Liao</surname><order>4</order></author><author><firstname>Shuai</firstname><surname>Li</surname><orcid>0000-0001-8316-5289</orcid><order>5</order></author><author><firstname>Yang</firstname><surname>Rong</surname><orcid>0000-0002-2335-2805</orcid><order>6</order></author><author><firstname>Zheyu</firstname><surname>Liu</surname><order>7</order></author><author><firstname>Zhijie</firstname><surname>Liu</surname><order>8</order></author><author><firstname>Kunhuang</firstname><surname>Lin</surname><order>9</order></author></authors><documents><document><filename>62487__26460__799ab671c5194eafaa3414aaf56d7530.pdf</filename><originalFilename>62487.pdf</originalFilename><uploaded>2023-02-03T11:41:37.9276438</uploaded><type>Output</type><contentLength>1228343</contentLength><contentType>application/pdf</contentType><version>Version of Record</version><cronfaStatus>true</cronfaStatus><documentNotes>This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license</documentNotes><copyrightCorrect>true</copyrightCorrect><language>eng</language><licence>https://creativecommons.org/licenses/by/4.0/</licence></document></documents><OutputDurs/></rfc1807>
spelling 2023-03-02T14:33:30.8271616 v2 62487 2023-02-03 A Novel Zeroing Neural Network for Solving Time-Varying Quadratic Matrix Equations against Linear Noises 94f19a09e17bad497ef1b4a0992c1d56 Zhan Li Zhan Li true false 42ff9eed09bcd109fbbe484a0f99a8a8 0000-0001-8316-5289 Shuai Li Shuai Li true false 2023-02-03 SCS The solving of quadratic matrix equations is a fundamental issue which essentially exists in the optimal control domain. However, noises exerted on the coefficients of quadratic matrix equations may affect the accuracy of the solutions. In order to solve the time-varying quadratic matrix equation problem under linear noise, a new error-processing design formula is proposed, and a resultant novel zeroing neural network model is developed. The new design formula incorporates a second-order error-processing manner, and the double-integration-enhanced zeroing neural network (DIEZNN) model is further proposed for solving time-varying quadratic matrix equations subject to linear noises. Compared with the original zeroing neural network (OZNN) model, finite-time zeroing neural network (FTZNN) model and integration-enhanced zeroing neural network (IEZNN) model, the DIEZNN model shows the superiority of its solution under linear noise; that is, when solving the problem of a time-varying quadratic matrix equation in the environment of linear noise, the residual error of the existing model will maintain a large level due to the influence of linear noise, which will eventually lead to the solution’s failure. The newly proposed DIEZNN model can guarantee a normal solution to the time-varying quadratic matrix equation task no matter how much linear noise there is. In addition, the theoretical analysis proves that the neural state of the DIEZNN model can converge to the theoretical solution even under linear noise. The computer simulation results further substantiate the superiority of the DIEZNN model in solving time-varying quadratic matrix equations under linear noise. Journal Article Mathematics 11 2 475 MDPI AG 2227-7390 time-varying quadratic matrix equation; double-integration-enhanced zeroing neural network; linear noise 16 1 2023 2023-01-16 10.3390/math11020475 COLLEGE NANME Computer Science COLLEGE CODE SCS Swansea University This study was supported in part by the National Natural Science Foundation of China (61962023 and 62066015) 2023-03-02T14:33:30.8271616 2023-02-03T11:38:55.4475639 Faculty of Science and Engineering School of Mathematics and Computer Science - Computer Science Jianfeng Li 1 Linxi Qu 2 Zhan Li 3 Bolin Liao 4 Shuai Li 0000-0001-8316-5289 5 Yang Rong 0000-0002-2335-2805 6 Zheyu Liu 7 Zhijie Liu 8 Kunhuang Lin 9 62487__26460__799ab671c5194eafaa3414aaf56d7530.pdf 62487.pdf 2023-02-03T11:41:37.9276438 Output 1228343 application/pdf Version of Record true 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 A Novel Zeroing Neural Network for Solving Time-Varying Quadratic Matrix Equations against Linear Noises
spellingShingle A Novel Zeroing Neural Network for Solving Time-Varying Quadratic Matrix Equations against Linear Noises
Zhan Li
Shuai Li
title_short A Novel Zeroing Neural Network for Solving Time-Varying Quadratic Matrix Equations against Linear Noises
title_full A Novel Zeroing Neural Network for Solving Time-Varying Quadratic Matrix Equations against Linear Noises
title_fullStr A Novel Zeroing Neural Network for Solving Time-Varying Quadratic Matrix Equations against Linear Noises
title_full_unstemmed A Novel Zeroing Neural Network for Solving Time-Varying Quadratic Matrix Equations against Linear Noises
title_sort A Novel Zeroing Neural Network for Solving Time-Varying Quadratic Matrix Equations against Linear Noises
author_id_str_mv 94f19a09e17bad497ef1b4a0992c1d56
42ff9eed09bcd109fbbe484a0f99a8a8
author_id_fullname_str_mv 94f19a09e17bad497ef1b4a0992c1d56_***_Zhan Li
42ff9eed09bcd109fbbe484a0f99a8a8_***_Shuai Li
author Zhan Li
Shuai Li
author2 Jianfeng Li
Linxi Qu
Zhan Li
Bolin Liao
Shuai Li
Yang Rong
Zheyu Liu
Zhijie Liu
Kunhuang Lin
format Journal article
container_title Mathematics
container_volume 11
container_issue 2
container_start_page 475
publishDate 2023
institution Swansea University
issn 2227-7390
doi_str_mv 10.3390/math11020475
publisher MDPI AG
college_str Faculty of Science and Engineering
hierarchytype
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 Mathematics and Computer Science - Computer Science{{{_:::_}}}Faculty of Science and Engineering{{{_:::_}}}School of Mathematics and Computer Science - Computer Science
document_store_str 1
active_str 0
description The solving of quadratic matrix equations is a fundamental issue which essentially exists in the optimal control domain. However, noises exerted on the coefficients of quadratic matrix equations may affect the accuracy of the solutions. In order to solve the time-varying quadratic matrix equation problem under linear noise, a new error-processing design formula is proposed, and a resultant novel zeroing neural network model is developed. The new design formula incorporates a second-order error-processing manner, and the double-integration-enhanced zeroing neural network (DIEZNN) model is further proposed for solving time-varying quadratic matrix equations subject to linear noises. Compared with the original zeroing neural network (OZNN) model, finite-time zeroing neural network (FTZNN) model and integration-enhanced zeroing neural network (IEZNN) model, the DIEZNN model shows the superiority of its solution under linear noise; that is, when solving the problem of a time-varying quadratic matrix equation in the environment of linear noise, the residual error of the existing model will maintain a large level due to the influence of linear noise, which will eventually lead to the solution’s failure. The newly proposed DIEZNN model can guarantee a normal solution to the time-varying quadratic matrix equation task no matter how much linear noise there is. In addition, the theoretical analysis proves that the neural state of the DIEZNN model can converge to the theoretical solution even under linear noise. The computer simulation results further substantiate the superiority of the DIEZNN model in solving time-varying quadratic matrix equations under linear noise.
published_date 2023-01-16T04:22:08Z
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score 11.012678

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