Backstepping State Feedback Regulator Design for an Unstable Reaction-Diffusion PDE with Long Time Delay
We consider the output regulation of an unstable reaction-diffusion PDE in the presence of regulator delay and unmatched disturbances, which are generated by an exosystem. The systematic design procedure of a backstepping state feedback regulator is first presented by mapping the reaction-diffusion...
Gespeichert in:
| Veröffentlicht in: | Journal of dynamical and control systems 2018-10, Vol.24 (4), p.563-576 |
|---|---|
| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | eng |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| container_end_page | 576 |
|---|---|
| container_issue | 4 |
| container_start_page | 563 |
| container_title | Journal of dynamical and control systems |
| container_volume | 24 |
| creator | Gu, Jian-Jun Wang, Jun-Min |
| description | We consider the output regulation of an unstable reaction-diffusion PDE in the presence of regulator delay and unmatched disturbances, which are generated by an exosystem. The systematic design procedure of a backstepping state feedback regulator is first presented by mapping the reaction-diffusion PDE cascaded with a transport equation into an error system, which is shown to be exponentially stable with a prescribed rate in a suitable Hilbert space. The regulator design relies on solving regulator equations, and the solvability condition of the regulator equations is then characterized by a transfer function and eigenvalues of the exosystem. Finally, the numerical simulations are provided to illustrate the effect of the regulator. |
| doi_str_mv | 10.1007/s10883-017-9384-5 |
| format | Article |
| fullrecord | <record><control><sourceid>proquest_cross</sourceid><recordid>TN_cdi_proquest_journals_2086321120</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>2086321120</sourcerecordid><originalsourceid>FETCH-LOGICAL-c316t-9fa05265390b679e38b21f4b17e2301ef6cff1808cfb03f373e554f924d8a5b3</originalsourceid><addsrcrecordid>eNp1kF1LwzAYhYsoOKc_wLuA19E3SdOkl7oPFQaKzuuQdknX2bU1SZH9ezMqeOVVDuE554UnSa4J3BIAcecJSMkwEIFzJlPMT5IJ4YJhmeXyNGYQOaaCpufJhfc7AMglk5Nk-6DLTx9M39dthd6DDgYtjdkU8Ru9mWpodOgcmhtfVy2yMeoWfbQ-6KIxEdBlqLsWz2trBx8Tep0v0HcdtmjVxcF1vTex3OjDZXJmdePN1e87TdbLxXr2hFcvj8-z-xUuGckCzq0GTjPOcigykRsmC0psWhBhKANibFZaSyTI0hbALBPMcJ7anKYbqXnBpsnNONu77mswPqhdN7g2XlQUZMYoIRQiRUaqdJ33zljVu3qv3UERUEefavSpok919Kl47NCx4yPbVsb9Lf9f-gEMT3ef</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>2086321120</pqid></control><display><type>article</type><title>Backstepping State Feedback Regulator Design for an Unstable Reaction-Diffusion PDE with Long Time Delay</title><source>Springer Nature - Complete Springer Journals</source><creator>Gu, Jian-Jun ; Wang, Jun-Min</creator><creatorcontrib>Gu, Jian-Jun ; Wang, Jun-Min</creatorcontrib><description>We consider the output regulation of an unstable reaction-diffusion PDE in the presence of regulator delay and unmatched disturbances, which are generated by an exosystem. The systematic design procedure of a backstepping state feedback regulator is first presented by mapping the reaction-diffusion PDE cascaded with a transport equation into an error system, which is shown to be exponentially stable with a prescribed rate in a suitable Hilbert space. The regulator design relies on solving regulator equations, and the solvability condition of the regulator equations is then characterized by a transfer function and eigenvalues of the exosystem. Finally, the numerical simulations are provided to illustrate the effect of the regulator.</description><identifier>ISSN: 1079-2724</identifier><identifier>EISSN: 1573-8698</identifier><identifier>DOI: 10.1007/s10883-017-9384-5</identifier><language>eng</language><publisher>New York: Springer US</publisher><subject>Calculus of Variations and Optimal Control; Optimization ; Computer simulation ; Control ; Delay ; Diffusion ; Dynamical Systems ; Dynamical Systems and Ergodic Theory ; Eigenvalues ; Hilbert space ; Mathematical analysis ; Mathematics ; Mathematics and Statistics ; State feedback ; Systems Theory ; Time lag ; Transfer functions ; Vibration</subject><ispartof>Journal of dynamical and control systems, 2018-10, Vol.24 (4), p.563-576</ispartof><rights>Springer Science+Business Media, LLC 2017</rights><rights>Copyright Springer Science & Business Media 2018</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c316t-9fa05265390b679e38b21f4b17e2301ef6cff1808cfb03f373e554f924d8a5b3</citedby><cites>FETCH-LOGICAL-c316t-9fa05265390b679e38b21f4b17e2301ef6cff1808cfb03f373e554f924d8a5b3</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.1007/s10883-017-9384-5$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/s10883-017-9384-5$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>314,776,780,27903,27904,41467,42536,51297</link.rule.ids></links><search><creatorcontrib>Gu, Jian-Jun</creatorcontrib><creatorcontrib>Wang, Jun-Min</creatorcontrib><title>Backstepping State Feedback Regulator Design for an Unstable Reaction-Diffusion PDE with Long Time Delay</title><title>Journal of dynamical and control systems</title><addtitle>J Dyn Control Syst</addtitle><description>We consider the output regulation of an unstable reaction-diffusion PDE in the presence of regulator delay and unmatched disturbances, which are generated by an exosystem. The systematic design procedure of a backstepping state feedback regulator is first presented by mapping the reaction-diffusion PDE cascaded with a transport equation into an error system, which is shown to be exponentially stable with a prescribed rate in a suitable Hilbert space. The regulator design relies on solving regulator equations, and the solvability condition of the regulator equations is then characterized by a transfer function and eigenvalues of the exosystem. Finally, the numerical simulations are provided to illustrate the effect of the regulator.</description><subject>Calculus of Variations and Optimal Control; Optimization</subject><subject>Computer simulation</subject><subject>Control</subject><subject>Delay</subject><subject>Diffusion</subject><subject>Dynamical Systems</subject><subject>Dynamical Systems and Ergodic Theory</subject><subject>Eigenvalues</subject><subject>Hilbert space</subject><subject>Mathematical analysis</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>State feedback</subject><subject>Systems Theory</subject><subject>Time lag</subject><subject>Transfer functions</subject><subject>Vibration</subject><issn>1079-2724</issn><issn>1573-8698</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2018</creationdate><recordtype>article</recordtype><recordid>eNp1kF1LwzAYhYsoOKc_wLuA19E3SdOkl7oPFQaKzuuQdknX2bU1SZH9ezMqeOVVDuE554UnSa4J3BIAcecJSMkwEIFzJlPMT5IJ4YJhmeXyNGYQOaaCpufJhfc7AMglk5Nk-6DLTx9M39dthd6DDgYtjdkU8Ru9mWpodOgcmhtfVy2yMeoWfbQ-6KIxEdBlqLsWz2trBx8Tep0v0HcdtmjVxcF1vTex3OjDZXJmdePN1e87TdbLxXr2hFcvj8-z-xUuGckCzq0GTjPOcigykRsmC0psWhBhKANibFZaSyTI0hbALBPMcJ7anKYbqXnBpsnNONu77mswPqhdN7g2XlQUZMYoIRQiRUaqdJ33zljVu3qv3UERUEefavSpok919Kl47NCx4yPbVsb9Lf9f-gEMT3ef</recordid><startdate>20181001</startdate><enddate>20181001</enddate><creator>Gu, Jian-Jun</creator><creator>Wang, Jun-Min</creator><general>Springer US</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope></search><sort><creationdate>20181001</creationdate><title>Backstepping State Feedback Regulator Design for an Unstable Reaction-Diffusion PDE with Long Time Delay</title><author>Gu, Jian-Jun ; Wang, Jun-Min</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c316t-9fa05265390b679e38b21f4b17e2301ef6cff1808cfb03f373e554f924d8a5b3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2018</creationdate><topic>Calculus of Variations and Optimal Control; Optimization</topic><topic>Computer simulation</topic><topic>Control</topic><topic>Delay</topic><topic>Diffusion</topic><topic>Dynamical Systems</topic><topic>Dynamical Systems and Ergodic Theory</topic><topic>Eigenvalues</topic><topic>Hilbert space</topic><topic>Mathematical analysis</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>State feedback</topic><topic>Systems Theory</topic><topic>Time lag</topic><topic>Transfer functions</topic><topic>Vibration</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Gu, Jian-Jun</creatorcontrib><creatorcontrib>Wang, Jun-Min</creatorcontrib><collection>CrossRef</collection><jtitle>Journal of dynamical and control systems</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Gu, Jian-Jun</au><au>Wang, Jun-Min</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Backstepping State Feedback Regulator Design for an Unstable Reaction-Diffusion PDE with Long Time Delay</atitle><jtitle>Journal of dynamical and control systems</jtitle><stitle>J Dyn Control Syst</stitle><date>2018-10-01</date><risdate>2018</risdate><volume>24</volume><issue>4</issue><spage>563</spage><epage>576</epage><pages>563-576</pages><issn>1079-2724</issn><eissn>1573-8698</eissn><abstract>We consider the output regulation of an unstable reaction-diffusion PDE in the presence of regulator delay and unmatched disturbances, which are generated by an exosystem. The systematic design procedure of a backstepping state feedback regulator is first presented by mapping the reaction-diffusion PDE cascaded with a transport equation into an error system, which is shown to be exponentially stable with a prescribed rate in a suitable Hilbert space. The regulator design relies on solving regulator equations, and the solvability condition of the regulator equations is then characterized by a transfer function and eigenvalues of the exosystem. Finally, the numerical simulations are provided to illustrate the effect of the regulator.</abstract><cop>New York</cop><pub>Springer US</pub><doi>10.1007/s10883-017-9384-5</doi><tpages>14</tpages></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 1079-2724 |
| ispartof | Journal of dynamical and control systems, 2018-10, Vol.24 (4), p.563-576 |
| issn | 1079-2724 1573-8698 |
| language | eng |
| recordid | cdi_proquest_journals_2086321120 |
| source | Springer Nature - Complete Springer Journals |
| subjects | Calculus of Variations and Optimal Control Optimization Computer simulation Control Delay Diffusion Dynamical Systems Dynamical Systems and Ergodic Theory Eigenvalues Hilbert space Mathematical analysis Mathematics Mathematics and Statistics State feedback Systems Theory Time lag Transfer functions Vibration |
| title | Backstepping State Feedback Regulator Design for an Unstable Reaction-Diffusion PDE with Long Time Delay |
| url | https://sfx.bib-bvb.de/sfx_tum?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2025-01-24T05%3A20%3A55IST&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=Backstepping%20State%20Feedback%20Regulator%20Design%20for%20an%20Unstable%20Reaction-Diffusion%20PDE%20with%20Long%20Time%20Delay&rft.jtitle=Journal%20of%20dynamical%20and%20control%20systems&rft.au=Gu,%20Jian-Jun&rft.date=2018-10-01&rft.volume=24&rft.issue=4&rft.spage=563&rft.epage=576&rft.pages=563-576&rft.issn=1079-2724&rft.eissn=1573-8698&rft_id=info:doi/10.1007/s10883-017-9384-5&rft_dat=%3Cproquest_cross%3E2086321120%3C/proquest_cross%3E%3Curl%3E%3C/url%3E&disable_directlink=true&sfx.directlink=off&sfx.report_link=0&rft_id=info:oai/&rft_pqid=2086321120&rft_id=info:pmid/&rfr_iscdi=true |