A New Varying-Parameter Recurrent Neural-Network for Online Solution of Time-Varying Sylvester Equation

Solving Sylvester equation is a common algebraic problem in mathematics and control theory. Different from the traditional fixed-parameter recurrent neural networks, such as gradient-based recurrent neural networks or Zhang neural networks, a novel varying-parameter recurrent neural network, [called...

Full description

Saved in:
Bibliographic Details
Published in:IEEE transactions on cybernetics 2018-11, Vol.48 (11), p.3135-3148
Main Authors: Zhang, Zhijun, Zheng, Lunan, Weng, Jian, Mao, Yijun, Lu, Wei, Xiao, Lin
Format: Article
Language:English
Subjects:
Biological neural networks
Computer simulation
Computer simulations
Control theory
Convergence
convergence and robustness
Mathematical analysis
Mathematical model
Neural networks
Parameters
Recurrent neural networks
Robustness
Robustness (mathematics)
time-varying equation solving
Time-varying systems
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
cited_by cdi_FETCH-LOGICAL-c349t-feb32783ea3c6a33d3e802dc906e8f4ef1eedd29cb738d936ebe7362f56a75123
cites cdi_FETCH-LOGICAL-c349t-feb32783ea3c6a33d3e802dc906e8f4ef1eedd29cb738d936ebe7362f56a75123
container_end_page 3148
container_issue 11
container_start_page 3135
container_title IEEE transactions on cybernetics
container_volume 48
creator Zhang, Zhijun
Zheng, Lunan
Weng, Jian
Mao, Yijun
Lu, Wei
Xiao, Lin
description Solving Sylvester equation is a common algebraic problem in mathematics and control theory. Different from the traditional fixed-parameter recurrent neural networks, such as gradient-based recurrent neural networks or Zhang neural networks, a novel varying-parameter recurrent neural network, [called varying-parameter convergent-differential neural network (VP-CDNN)] is proposed in this paper for obtaining the online solution to the time-varying Sylvester equation. With time passing by, this kind of new varying-parameter neural network can achieve super-exponential performance. Computer simulation comparisons between the fixed-parameter neural networks and the proposed VP-CDNN via using different kinds of activation functions demonstrate that the proposed VP-CDNN has better convergence and robustness properties.
doi_str_mv 10.1109/TCYB.2017.2760883
format article
fullrecord <record><control><sourceid>proquest_cross</sourceid><recordid>TN_cdi_crossref_primary_10_1109_TCYB_2017_2760883</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><ieee_id>8283812</ieee_id><sourcerecordid>2121931766</sourcerecordid><originalsourceid>FETCH-LOGICAL-c349t-feb32783ea3c6a33d3e802dc906e8f4ef1eedd29cb738d936ebe7362f56a75123</originalsourceid><addsrcrecordid>eNpdkU1LAzEQhoMoWtQfIIIEvHjZmmTafBy1-AWlilbBU0h3Z2Xr7kazu4r_3iytPZjLhLzPvEzmJeSIsyHnzJzPJ6-XQ8G4GgolmdawRQaCS50Iocbbm7tUe-SwaZYsHh2fjN4le8IYMwLNB-Ttgs7wm7648FPUb8mDC67CFgN9xLQLAes26l1wZTLD9tuHd5r7QO_rsqiRPvmyawtfU5_TeVFhsrahTz_lFza9zdVn53rkgOzkrmzwcF33yfP11Xxym0zvb-4mF9MkhZFpkxwXIJQGdJBKB5ABaiay1DCJOh9hzhGzTJh0oUBnBiQuUIEU-Vg6NeYC9snZyvcj-M8uzmCrokmxLF2NvmusYFIDGM5GET39hy59F-o4nRVccANcSRkpvqLS4JsmYG4_QlHFf1rObB-E7YOwfRB2HUTsOVk7d4sKs03H39ojcLwCCkTcyFroKAr4BboYjJI</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>2121931766</pqid></control><display><type>article</type><title>A New Varying-Parameter Recurrent Neural-Network for Online Solution of Time-Varying Sylvester Equation</title><source>IEEE Xplore (Online service)</source><creator>Zhang, Zhijun ; Zheng, Lunan ; Weng, Jian ; Mao, Yijun ; Lu, Wei ; Xiao, Lin</creator><creatorcontrib>Zhang, Zhijun ; Zheng, Lunan ; Weng, Jian ; Mao, Yijun ; Lu, Wei ; Xiao, Lin</creatorcontrib><description>Solving Sylvester equation is a common algebraic problem in mathematics and control theory. Different from the traditional fixed-parameter recurrent neural networks, such as gradient-based recurrent neural networks or Zhang neural networks, a novel varying-parameter recurrent neural network, [called varying-parameter convergent-differential neural network (VP-CDNN)] is proposed in this paper for obtaining the online solution to the time-varying Sylvester equation. With time passing by, this kind of new varying-parameter neural network can achieve super-exponential performance. Computer simulation comparisons between the fixed-parameter neural networks and the proposed VP-CDNN via using different kinds of activation functions demonstrate that the proposed VP-CDNN has better convergence and robustness properties.</description><identifier>ISSN: 2168-2267</identifier><identifier>EISSN: 2168-2275</identifier><identifier>DOI: 10.1109/TCYB.2017.2760883</identifier><identifier>PMID: 29994381</identifier><identifier>CODEN: ITCEB8</identifier><language>eng</language><publisher>United States: IEEE</publisher><subject>Biological neural networks ; Computer simulation ; Computer simulations ; Control theory ; Convergence ; convergence and robustness ; Mathematical analysis ; Mathematical model ; Neural networks ; Parameters ; Recurrent neural networks ; Robustness ; Robustness (mathematics) ; time-varying equation solving ; Time-varying systems</subject><ispartof>IEEE transactions on cybernetics, 2018-11, Vol.48 (11), p.3135-3148</ispartof><rights>Copyright The Institute of Electrical and Electronics Engineers, Inc. (IEEE) 2018</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c349t-feb32783ea3c6a33d3e802dc906e8f4ef1eedd29cb738d936ebe7362f56a75123</citedby><cites>FETCH-LOGICAL-c349t-feb32783ea3c6a33d3e802dc906e8f4ef1eedd29cb738d936ebe7362f56a75123</cites><orcidid>0000-0003-4067-8230 ; 0000-0002-4068-1766 ; 0000-0002-6859-3426 ; 0000-0002-7671-6051 ; 0000-0003-3172-3490</orcidid></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktohtml>$$Uhttps://ieeexplore.ieee.org/document/8283812$$EHTML$$P50$$Gieee$$H</linktohtml><link.rule.ids>314,780,784,27924,27925,54796</link.rule.ids><backlink>$$Uhttps://www.ncbi.nlm.nih.gov/pubmed/29994381$$D View this record in MEDLINE/PubMed$$Hfree_for_read</backlink></links><search><creatorcontrib>Zhang, Zhijun</creatorcontrib><creatorcontrib>Zheng, Lunan</creatorcontrib><creatorcontrib>Weng, Jian</creatorcontrib><creatorcontrib>Mao, Yijun</creatorcontrib><creatorcontrib>Lu, Wei</creatorcontrib><creatorcontrib>Xiao, Lin</creatorcontrib><title>A New Varying-Parameter Recurrent Neural-Network for Online Solution of Time-Varying Sylvester Equation</title><title>IEEE transactions on cybernetics</title><addtitle>TCYB</addtitle><addtitle>IEEE Trans Cybern</addtitle><description>Solving Sylvester equation is a common algebraic problem in mathematics and control theory. Different from the traditional fixed-parameter recurrent neural networks, such as gradient-based recurrent neural networks or Zhang neural networks, a novel varying-parameter recurrent neural network, [called varying-parameter convergent-differential neural network (VP-CDNN)] is proposed in this paper for obtaining the online solution to the time-varying Sylvester equation. With time passing by, this kind of new varying-parameter neural network can achieve super-exponential performance. Computer simulation comparisons between the fixed-parameter neural networks and the proposed VP-CDNN via using different kinds of activation functions demonstrate that the proposed VP-CDNN has better convergence and robustness properties.</description><subject>Biological neural networks</subject><subject>Computer simulation</subject><subject>Computer simulations</subject><subject>Control theory</subject><subject>Convergence</subject><subject>convergence and robustness</subject><subject>Mathematical analysis</subject><subject>Mathematical model</subject><subject>Neural networks</subject><subject>Parameters</subject><subject>Recurrent neural networks</subject><subject>Robustness</subject><subject>Robustness (mathematics)</subject><subject>time-varying equation solving</subject><subject>Time-varying systems</subject><issn>2168-2267</issn><issn>2168-2275</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2018</creationdate><recordtype>article</recordtype><recordid>eNpdkU1LAzEQhoMoWtQfIIIEvHjZmmTafBy1-AWlilbBU0h3Z2Xr7kazu4r_3iytPZjLhLzPvEzmJeSIsyHnzJzPJ6-XQ8G4GgolmdawRQaCS50Iocbbm7tUe-SwaZYsHh2fjN4le8IYMwLNB-Ttgs7wm7648FPUb8mDC67CFgN9xLQLAes26l1wZTLD9tuHd5r7QO_rsqiRPvmyawtfU5_TeVFhsrahTz_lFza9zdVn53rkgOzkrmzwcF33yfP11Xxym0zvb-4mF9MkhZFpkxwXIJQGdJBKB5ABaiay1DCJOh9hzhGzTJh0oUBnBiQuUIEU-Vg6NeYC9snZyvcj-M8uzmCrokmxLF2NvmusYFIDGM5GET39hy59F-o4nRVccANcSRkpvqLS4JsmYG4_QlHFf1rObB-E7YOwfRB2HUTsOVk7d4sKs03H39ojcLwCCkTcyFroKAr4BboYjJI</recordid><startdate>20181101</startdate><enddate>20181101</enddate><creator>Zhang, Zhijun</creator><creator>Zheng, Lunan</creator><creator>Weng, Jian</creator><creator>Mao, Yijun</creator><creator>Lu, Wei</creator><creator>Xiao, Lin</creator><general>IEEE</general><general>The Institute of Electrical and Electronics Engineers, Inc. (IEEE)</general><scope>97E</scope><scope>RIA</scope><scope>RIE</scope><scope>NPM</scope><scope>AAYXX</scope><scope>CITATION</scope><scope>7SC</scope><scope>7SP</scope><scope>7TB</scope><scope>8FD</scope><scope>F28</scope><scope>FR3</scope><scope>H8D</scope><scope>JQ2</scope><scope>L7M</scope><scope>L~C</scope><scope>L~D</scope><scope>7X8</scope><orcidid>https://orcid.org/0000-0003-4067-8230</orcidid><orcidid>https://orcid.org/0000-0002-4068-1766</orcidid><orcidid>https://orcid.org/0000-0002-6859-3426</orcidid><orcidid>https://orcid.org/0000-0002-7671-6051</orcidid><orcidid>https://orcid.org/0000-0003-3172-3490</orcidid></search><sort><creationdate>20181101</creationdate><title>A New Varying-Parameter Recurrent Neural-Network for Online Solution of Time-Varying Sylvester Equation</title><author>Zhang, Zhijun ; Zheng, Lunan ; Weng, Jian ; Mao, Yijun ; Lu, Wei ; Xiao, Lin</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c349t-feb32783ea3c6a33d3e802dc906e8f4ef1eedd29cb738d936ebe7362f56a75123</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2018</creationdate><topic>Biological neural networks</topic><topic>Computer simulation</topic><topic>Computer simulations</topic><topic>Control theory</topic><topic>Convergence</topic><topic>convergence and robustness</topic><topic>Mathematical analysis</topic><topic>Mathematical model</topic><topic>Neural networks</topic><topic>Parameters</topic><topic>Recurrent neural networks</topic><topic>Robustness</topic><topic>Robustness (mathematics)</topic><topic>time-varying equation solving</topic><topic>Time-varying systems</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Zhang, Zhijun</creatorcontrib><creatorcontrib>Zheng, Lunan</creatorcontrib><creatorcontrib>Weng, Jian</creatorcontrib><creatorcontrib>Mao, Yijun</creatorcontrib><creatorcontrib>Lu, Wei</creatorcontrib><creatorcontrib>Xiao, Lin</creatorcontrib><collection>IEEE All-Society Periodicals Package (ASPP) 2005-present</collection><collection>IEEE All-Society Periodicals Package (ASPP) 1998-Present</collection><collection>IEEE Xplore</collection><collection>PubMed</collection><collection>CrossRef</collection><collection>Computer and Information Systems Abstracts</collection><collection>Electronics &amp; Communications Abstracts</collection><collection>Mechanical &amp; Transportation Engineering Abstracts</collection><collection>Technology Research Database</collection><collection>ANTE: Abstracts in New Technology &amp; Engineering</collection><collection>Engineering Research Database</collection><collection>Aerospace Database</collection><collection>ProQuest Computer Science Collection</collection><collection>Advanced Technologies Database with Aerospace</collection><collection>Computer and Information Systems Abstracts – Academic</collection><collection>Computer and Information Systems Abstracts Professional</collection><collection>MEDLINE - Academic</collection><jtitle>IEEE transactions on cybernetics</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Zhang, Zhijun</au><au>Zheng, Lunan</au><au>Weng, Jian</au><au>Mao, Yijun</au><au>Lu, Wei</au><au>Xiao, Lin</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>A New Varying-Parameter Recurrent Neural-Network for Online Solution of Time-Varying Sylvester Equation</atitle><jtitle>IEEE transactions on cybernetics</jtitle><stitle>TCYB</stitle><addtitle>IEEE Trans Cybern</addtitle><date>2018-11-01</date><risdate>2018</risdate><volume>48</volume><issue>11</issue><spage>3135</spage><epage>3148</epage><pages>3135-3148</pages><issn>2168-2267</issn><eissn>2168-2275</eissn><coden>ITCEB8</coden><abstract>Solving Sylvester equation is a common algebraic problem in mathematics and control theory. Different from the traditional fixed-parameter recurrent neural networks, such as gradient-based recurrent neural networks or Zhang neural networks, a novel varying-parameter recurrent neural network, [called varying-parameter convergent-differential neural network (VP-CDNN)] is proposed in this paper for obtaining the online solution to the time-varying Sylvester equation. With time passing by, this kind of new varying-parameter neural network can achieve super-exponential performance. Computer simulation comparisons between the fixed-parameter neural networks and the proposed VP-CDNN via using different kinds of activation functions demonstrate that the proposed VP-CDNN has better convergence and robustness properties.</abstract><cop>United States</cop><pub>IEEE</pub><pmid>29994381</pmid><doi>10.1109/TCYB.2017.2760883</doi><tpages>14</tpages><orcidid>https://orcid.org/0000-0003-4067-8230</orcidid><orcidid>https://orcid.org/0000-0002-4068-1766</orcidid><orcidid>https://orcid.org/0000-0002-6859-3426</orcidid><orcidid>https://orcid.org/0000-0002-7671-6051</orcidid><orcidid>https://orcid.org/0000-0003-3172-3490</orcidid></addata></record>
fulltext fulltext
identifier ISSN: 2168-2267
ispartof IEEE transactions on cybernetics, 2018-11, Vol.48 (11), p.3135-3148
issn 2168-2267
2168-2275
language eng
recordid cdi_crossref_primary_10_1109_TCYB_2017_2760883
source IEEE Xplore (Online service)
subjects Biological neural networks
Computer simulation
Computer simulations
Control theory
Convergence
convergence and robustness
Mathematical analysis
Mathematical model
Neural networks
Parameters
Recurrent neural networks
Robustness
Robustness (mathematics)
time-varying equation solving
Time-varying systems
title A New Varying-Parameter Recurrent Neural-Network for Online Solution of Time-Varying Sylvester Equation
url http://sfxeu10.hosted.exlibrisgroup.com/loughborough?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2024-12-30T21%3A51%3A58IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-proquest_cross&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=A%20New%20Varying-Parameter%20Recurrent%20Neural-Network%20for%20Online%20Solution%20of%20Time-Varying%20Sylvester%20Equation&rft.jtitle=IEEE%20transactions%20on%20cybernetics&rft.au=Zhang,%20Zhijun&rft.date=2018-11-01&rft.volume=48&rft.issue=11&rft.spage=3135&rft.epage=3148&rft.pages=3135-3148&rft.issn=2168-2267&rft.eissn=2168-2275&rft.coden=ITCEB8&rft_id=info:doi/10.1109/TCYB.2017.2760883&rft_dat=%3Cproquest_cross%3E2121931766%3C/proquest_cross%3E%3Cgrp_id%3Ecdi_FETCH-LOGICAL-c349t-feb32783ea3c6a33d3e802dc906e8f4ef1eedd29cb738d936ebe7362f56a75123%3C/grp_id%3E%3Coa%3E%3C/oa%3E%3Curl%3E%3C/url%3E&rft_id=info:oai/&rft_pqid=2121931766&rft_id=info:pmid/29994381&rft_ieee_id=8283812&rfr_iscdi=true