Dynamic stabilization for a cascaded beam PDE–ODE system with boundary disturbance

We are concerned with the dynamic stabilization for a cascaded Euler–Bernoulli beam (EBB) partial differential equation (PDE)–ordinary differential equation (ODE) system subject to boundary control and matched internal uncertainty and external disturbance. State feedback stabilization of such system...

Full description

Saved in:
Bibliographic Details
Published in:Mathematical methods in the applied sciences 2023-06, Vol.46 (9), p.10167-10185
Main Author: Mei, Zhan‐Dong
Format: Article
Language:English
Subjects:
Boundary control
cascaded PDE–ODE system
Control theory
disturbance estimator
Euler-Bernoulli beams
Euler–Bernoulli beam equation
exponential stabilization
Feedback control
Output feedback
Partial differential equations
Stabilization
State feedback
State observers
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-c2239-b75ccdb860cc3a8de371e66637b6718fcbacec5998e1e1deba2d1f3a697b54733
cites cdi_FETCH-LOGICAL-c2239-b75ccdb860cc3a8de371e66637b6718fcbacec5998e1e1deba2d1f3a697b54733
container_end_page 10185
container_issue 9
container_start_page 10167
container_title Mathematical methods in the applied sciences
container_volume 46
creator Mei, Zhan‐Dong
description We are concerned with the dynamic stabilization for a cascaded Euler–Bernoulli beam (EBB) partial differential equation (PDE)–ordinary differential equation (ODE) system subject to boundary control and matched internal uncertainty and external disturbance. State feedback stabilization of such system without disturbance has been recently discussed by X.H. Wu, H. Feng (Sci China Inf Sci, 2022, 65(5): 159202). An infinite‐dimensional disturbance estimator is constructed in order to estimate the total disturbance. By compensating the total disturbance, we design a state observer to trace the state and then an estimated state and estimated total disturbance‐based output feedback control law. It is proved that the original system is exponentially stable, and other states of the closed‐loop are bounded. Some numerical simulations are presented.
doi_str_mv 10.1002/mma.9109
format article
fullrecord <record><control><sourceid>proquest_cross</sourceid><recordid>TN_cdi_proquest_journals_2812360813</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>2812360813</sourcerecordid><originalsourceid>FETCH-LOGICAL-c2239-b75ccdb860cc3a8de371e66637b6718fcbacec5998e1e1deba2d1f3a697b54733</originalsourceid><addsrcrecordid>eNp10LtOwzAUBmALgUQpSDyCJRaWFF9SOxmrXgCpVRnKbB1fIlw1SbETVWHiHXhDnoSUsrKcs3w6lx-hW0pGlBD2UJYwyinJz9Cgr3lCUynO0YBQSZKU0fQSXcW4JYRklLIB2sy6CkpvcGxA-53_gMbXFS7qgAEbiAass1g7KPHLbP79-bWezXHsYuNKfPDNG9Z1W1kIHbY-Nm3QUBl3jS4K2EV389eH6HUx30yfkuX68Xk6WSaGMZ4nWo6NsToTxBgOmXVcUieE4FILSbPCaDDOjPM8c9RR6zQwSwsOIpd6nErOh-juNHcf6vfWxUZt6zZU_UrFMsq46J88qvuTMqGOMbhC7YMv-5MVJeqYmeozU8fMepqc6MHvXPevU6vV5Nf_ALZZbk0</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>2812360813</pqid></control><display><type>article</type><title>Dynamic stabilization for a cascaded beam PDE–ODE system with boundary disturbance</title><source>Wiley</source><creator>Mei, Zhan‐Dong</creator><creatorcontrib>Mei, Zhan‐Dong</creatorcontrib><description>We are concerned with the dynamic stabilization for a cascaded Euler–Bernoulli beam (EBB) partial differential equation (PDE)–ordinary differential equation (ODE) system subject to boundary control and matched internal uncertainty and external disturbance. State feedback stabilization of such system without disturbance has been recently discussed by X.H. Wu, H. Feng (Sci China Inf Sci, 2022, 65(5): 159202). An infinite‐dimensional disturbance estimator is constructed in order to estimate the total disturbance. By compensating the total disturbance, we design a state observer to trace the state and then an estimated state and estimated total disturbance‐based output feedback control law. It is proved that the original system is exponentially stable, and other states of the closed‐loop are bounded. Some numerical simulations are presented.</description><identifier>ISSN: 0170-4214</identifier><identifier>EISSN: 1099-1476</identifier><identifier>DOI: 10.1002/mma.9109</identifier><language>eng</language><publisher>Freiburg: Wiley Subscription Services, Inc</publisher><subject>Boundary control ; cascaded PDE–ODE system ; Control theory ; disturbance estimator ; Euler-Bernoulli beams ; Euler–Bernoulli beam equation ; exponential stabilization ; Feedback control ; Output feedback ; Partial differential equations ; Stabilization ; State feedback ; State observers</subject><ispartof>Mathematical methods in the applied sciences, 2023-06, Vol.46 (9), p.10167-10185</ispartof><rights>2023 John Wiley &amp; Sons, Ltd.</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c2239-b75ccdb860cc3a8de371e66637b6718fcbacec5998e1e1deba2d1f3a697b54733</citedby><cites>FETCH-LOGICAL-c2239-b75ccdb860cc3a8de371e66637b6718fcbacec5998e1e1deba2d1f3a697b54733</cites><orcidid>0000-0001-7570-3921</orcidid></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>314,780,784,27924,27925</link.rule.ids></links><search><creatorcontrib>Mei, Zhan‐Dong</creatorcontrib><title>Dynamic stabilization for a cascaded beam PDE–ODE system with boundary disturbance</title><title>Mathematical methods in the applied sciences</title><description>We are concerned with the dynamic stabilization for a cascaded Euler–Bernoulli beam (EBB) partial differential equation (PDE)–ordinary differential equation (ODE) system subject to boundary control and matched internal uncertainty and external disturbance. State feedback stabilization of such system without disturbance has been recently discussed by X.H. Wu, H. Feng (Sci China Inf Sci, 2022, 65(5): 159202). An infinite‐dimensional disturbance estimator is constructed in order to estimate the total disturbance. By compensating the total disturbance, we design a state observer to trace the state and then an estimated state and estimated total disturbance‐based output feedback control law. It is proved that the original system is exponentially stable, and other states of the closed‐loop are bounded. Some numerical simulations are presented.</description><subject>Boundary control</subject><subject>cascaded PDE–ODE system</subject><subject>Control theory</subject><subject>disturbance estimator</subject><subject>Euler-Bernoulli beams</subject><subject>Euler–Bernoulli beam equation</subject><subject>exponential stabilization</subject><subject>Feedback control</subject><subject>Output feedback</subject><subject>Partial differential equations</subject><subject>Stabilization</subject><subject>State feedback</subject><subject>State observers</subject><issn>0170-4214</issn><issn>1099-1476</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2023</creationdate><recordtype>article</recordtype><recordid>eNp10LtOwzAUBmALgUQpSDyCJRaWFF9SOxmrXgCpVRnKbB1fIlw1SbETVWHiHXhDnoSUsrKcs3w6lx-hW0pGlBD2UJYwyinJz9Cgr3lCUynO0YBQSZKU0fQSXcW4JYRklLIB2sy6CkpvcGxA-53_gMbXFS7qgAEbiAass1g7KPHLbP79-bWezXHsYuNKfPDNG9Z1W1kIHbY-Nm3QUBl3jS4K2EV389eH6HUx30yfkuX68Xk6WSaGMZ4nWo6NsToTxBgOmXVcUieE4FILSbPCaDDOjPM8c9RR6zQwSwsOIpd6nErOh-juNHcf6vfWxUZt6zZU_UrFMsq46J88qvuTMqGOMbhC7YMv-5MVJeqYmeozU8fMepqc6MHvXPevU6vV5Nf_ALZZbk0</recordid><startdate>202306</startdate><enddate>202306</enddate><creator>Mei, Zhan‐Dong</creator><general>Wiley Subscription Services, Inc</general><scope>AAYXX</scope><scope>CITATION</scope><scope>7TB</scope><scope>8FD</scope><scope>FR3</scope><scope>JQ2</scope><scope>KR7</scope><orcidid>https://orcid.org/0000-0001-7570-3921</orcidid></search><sort><creationdate>202306</creationdate><title>Dynamic stabilization for a cascaded beam PDE–ODE system with boundary disturbance</title><author>Mei, Zhan‐Dong</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c2239-b75ccdb860cc3a8de371e66637b6718fcbacec5998e1e1deba2d1f3a697b54733</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2023</creationdate><topic>Boundary control</topic><topic>cascaded PDE–ODE system</topic><topic>Control theory</topic><topic>disturbance estimator</topic><topic>Euler-Bernoulli beams</topic><topic>Euler–Bernoulli beam equation</topic><topic>exponential stabilization</topic><topic>Feedback control</topic><topic>Output feedback</topic><topic>Partial differential equations</topic><topic>Stabilization</topic><topic>State feedback</topic><topic>State observers</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Mei, Zhan‐Dong</creatorcontrib><collection>CrossRef</collection><collection>Mechanical &amp; Transportation Engineering Abstracts</collection><collection>Technology Research Database</collection><collection>Engineering Research Database</collection><collection>ProQuest Computer Science Collection</collection><collection>Civil Engineering Abstracts</collection><jtitle>Mathematical methods in the applied sciences</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Mei, Zhan‐Dong</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Dynamic stabilization for a cascaded beam PDE–ODE system with boundary disturbance</atitle><jtitle>Mathematical methods in the applied sciences</jtitle><date>2023-06</date><risdate>2023</risdate><volume>46</volume><issue>9</issue><spage>10167</spage><epage>10185</epage><pages>10167-10185</pages><issn>0170-4214</issn><eissn>1099-1476</eissn><abstract>We are concerned with the dynamic stabilization for a cascaded Euler–Bernoulli beam (EBB) partial differential equation (PDE)–ordinary differential equation (ODE) system subject to boundary control and matched internal uncertainty and external disturbance. State feedback stabilization of such system without disturbance has been recently discussed by X.H. Wu, H. Feng (Sci China Inf Sci, 2022, 65(5): 159202). An infinite‐dimensional disturbance estimator is constructed in order to estimate the total disturbance. By compensating the total disturbance, we design a state observer to trace the state and then an estimated state and estimated total disturbance‐based output feedback control law. It is proved that the original system is exponentially stable, and other states of the closed‐loop are bounded. Some numerical simulations are presented.</abstract><cop>Freiburg</cop><pub>Wiley Subscription Services, Inc</pub><doi>10.1002/mma.9109</doi><tpages>19</tpages><orcidid>https://orcid.org/0000-0001-7570-3921</orcidid></addata></record>
fulltext fulltext
identifier ISSN: 0170-4214
ispartof Mathematical methods in the applied sciences, 2023-06, Vol.46 (9), p.10167-10185
issn 0170-4214
1099-1476
language eng
recordid cdi_proquest_journals_2812360813
source Wiley
subjects Boundary control
cascaded PDE–ODE system
Control theory
disturbance estimator
Euler-Bernoulli beams
Euler–Bernoulli beam equation
exponential stabilization
Feedback control
Output feedback
Partial differential equations
Stabilization
State feedback
State observers
title Dynamic stabilization for a cascaded beam PDE–ODE system with boundary disturbance
url http://sfxeu10.hosted.exlibrisgroup.com/loughborough?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2024-12-25T16%3A22%3A53IST&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=Dynamic%20stabilization%20for%20a%20cascaded%20beam%20PDE%E2%80%93ODE%20system%20with%20boundary%20disturbance&rft.jtitle=Mathematical%20methods%20in%20the%20applied%20sciences&rft.au=Mei,%20Zhan%E2%80%90Dong&rft.date=2023-06&rft.volume=46&rft.issue=9&rft.spage=10167&rft.epage=10185&rft.pages=10167-10185&rft.issn=0170-4214&rft.eissn=1099-1476&rft_id=info:doi/10.1002/mma.9109&rft_dat=%3Cproquest_cross%3E2812360813%3C/proquest_cross%3E%3Cgrp_id%3Ecdi_FETCH-LOGICAL-c2239-b75ccdb860cc3a8de371e66637b6718fcbacec5998e1e1deba2d1f3a697b54733%3C/grp_id%3E%3Coa%3E%3C/oa%3E%3Curl%3E%3C/url%3E&rft_id=info:oai/&rft_pqid=2812360813&rft_id=info:pmid/&rfr_iscdi=true