Boundary controllability of structural acoustic systems with variable coefficients and curved walls
This paper studies a structural acoustic model consisting of an interior acoustic wave equation with variable coefficients and a coupled Kirchhoff plate equation with a curved middle surface. By the Riemannian geometry approach and the multiplier technique, we establish exact controllability of the...
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| Veröffentlicht in: | Mathematics of control, signals, and systems signals, and systems, 2018-03, Vol.30 (1), p.1-28, Article 5 |
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| creator | Yang, Fengyan Yao, Pengfei Chen, Goong |
| description | This paper studies a structural acoustic model consisting of an interior acoustic wave equation with variable coefficients and a coupled Kirchhoff plate equation with a curved middle surface. By the Riemannian geometry approach and the multiplier technique, we establish exact controllability of the hybrid system under verifiable assumptions on the geometry of the interior domain and the interface boundary with two controls: One is a Neumann boundary control exerted on the wave equation, and the other acts on the interior of the plate equation. Furthermore, if the control for the plate equation is active alone, we prove that the hybrid system with partial Robin boundary condition of the wave equation is exactly controllable with the plate component and approximately controllable with the wave component. |
| doi_str_mv | 10.1007/s00498-018-0211-7 |
| format | Article |
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By the Riemannian geometry approach and the multiplier technique, we establish exact controllability of the hybrid system under verifiable assumptions on the geometry of the interior domain and the interface boundary with two controls: One is a Neumann boundary control exerted on the wave equation, and the other acts on the interior of the plate equation. Furthermore, if the control for the plate equation is active alone, we prove that the hybrid system with partial Robin boundary condition of the wave equation is exactly controllable with the plate component and approximately controllable with the wave component.</description><identifier>ISSN: 0932-4194</identifier><identifier>EISSN: 1435-568X</identifier><identifier>DOI: 10.1007/s00498-018-0211-7</identifier><language>eng</language><publisher>London: Springer London</publisher><subject>Acoustic coupling ; Acoustics ; Boundary control ; Communications Engineering ; Control ; Controllability ; Hybrid systems ; Mathematics ; Mathematics and Statistics ; Mechatronics ; Networks ; Original Article ; Plates (structural members) ; Robotics ; Stability ; Systems Theory ; Wave equations</subject><ispartof>Mathematics of control, signals, and systems, 2018-03, Vol.30 (1), p.1-28, Article 5</ispartof><rights>Springer-Verlag London Ltd., part of Springer Nature 2018</rights><rights>Mathematics of Control, Signals, and Systems is a copyright of Springer, (2018). All Rights Reserved.</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c316t-167d8fbdd92e78f5bd8800e4a325be0fc36e2bf19029e399e075e836734a1f403</citedby><cites>FETCH-LOGICAL-c316t-167d8fbdd92e78f5bd8800e4a325be0fc36e2bf19029e399e075e836734a1f403</cites><orcidid>0000-0002-2164-5217</orcidid></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.1007/s00498-018-0211-7$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/s00498-018-0211-7$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>314,776,780,27901,27902,41464,42533,51294</link.rule.ids></links><search><creatorcontrib>Yang, Fengyan</creatorcontrib><creatorcontrib>Yao, Pengfei</creatorcontrib><creatorcontrib>Chen, Goong</creatorcontrib><title>Boundary controllability of structural acoustic systems with variable coefficients and curved walls</title><title>Mathematics of control, signals, and systems</title><addtitle>Math. Control Signals Syst</addtitle><description>This paper studies a structural acoustic model consisting of an interior acoustic wave equation with variable coefficients and a coupled Kirchhoff plate equation with a curved middle surface. By the Riemannian geometry approach and the multiplier technique, we establish exact controllability of the hybrid system under verifiable assumptions on the geometry of the interior domain and the interface boundary with two controls: One is a Neumann boundary control exerted on the wave equation, and the other acts on the interior of the plate equation. Furthermore, if the control for the plate equation is active alone, we prove that the hybrid system with partial Robin boundary condition of the wave equation is exactly controllable with the plate component and approximately controllable with the wave component.</description><subject>Acoustic coupling</subject><subject>Acoustics</subject><subject>Boundary control</subject><subject>Communications Engineering</subject><subject>Control</subject><subject>Controllability</subject><subject>Hybrid systems</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Mechatronics</subject><subject>Networks</subject><subject>Original Article</subject><subject>Plates (structural members)</subject><subject>Robotics</subject><subject>Stability</subject><subject>Systems Theory</subject><subject>Wave equations</subject><issn>0932-4194</issn><issn>1435-568X</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2018</creationdate><recordtype>article</recordtype><sourceid>BENPR</sourceid><recordid>eNp1kE1LAzEQhoMoWKs_wFvA8-ok2d0kRy1-QcGLgreQzSaast3UJFvpvzelgicPw1ze553hQeiSwDUB4DcJoJaiAlKGElLxIzQjNWuqphXvx2gGktGqJrI-RWcprQCAtJzMkLkL09jruMMmjDmGYdCdH3ze4eBwynEyeYp6wNqEKWVvcNqlbNcJf_v8ibc6et0NtsDWOW-8HXPCeuyxmeLW9vhbD0M6RydOD8le_O45enu4f108VcuXx-fF7bIyjLS5Kg_1wnV9L6nlwjVdLwSArTWjTWfBGdZa2jkigUrLpLTAGytYy1mtiauBzdHVoXcTw9dkU1arMMWxnFQUiJQCar5PkUPKxJBStE5tol8XA4qA2rtUB5equFR7l4oXhh6YVLLjh41_zf9DPxHjeNc</recordid><startdate>20180301</startdate><enddate>20180301</enddate><creator>Yang, Fengyan</creator><creator>Yao, Pengfei</creator><creator>Chen, Goong</creator><general>Springer London</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope><scope>3V.</scope><scope>7SC</scope><scope>7SP</scope><scope>7WY</scope><scope>7WZ</scope><scope>7XB</scope><scope>87Z</scope><scope>88I</scope><scope>8AL</scope><scope>8AO</scope><scope>8FD</scope><scope>8FE</scope><scope>8FG</scope><scope>8FK</scope><scope>8FL</scope><scope>ABJCF</scope><scope>ABUWG</scope><scope>AFKRA</scope><scope>ARAPS</scope><scope>AZQEC</scope><scope>BENPR</scope><scope>BEZIV</scope><scope>BGLVJ</scope><scope>CCPQU</scope><scope>DWQXO</scope><scope>FRNLG</scope><scope>F~G</scope><scope>GNUQQ</scope><scope>HCIFZ</scope><scope>JQ2</scope><scope>K60</scope><scope>K6~</scope><scope>K7-</scope><scope>L.-</scope><scope>L6V</scope><scope>L7M</scope><scope>L~C</scope><scope>L~D</scope><scope>M0C</scope><scope>M0N</scope><scope>M2P</scope><scope>M7S</scope><scope>P5Z</scope><scope>P62</scope><scope>PQBIZ</scope><scope>PQBZA</scope><scope>PQEST</scope><scope>PQQKQ</scope><scope>PQUKI</scope><scope>PTHSS</scope><scope>PYYUZ</scope><scope>Q9U</scope><scope>S0W</scope><orcidid>https://orcid.org/0000-0002-2164-5217</orcidid></search><sort><creationdate>20180301</creationdate><title>Boundary controllability of structural acoustic systems with variable coefficients and curved walls</title><author>Yang, Fengyan ; Yao, Pengfei ; Chen, Goong</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c316t-167d8fbdd92e78f5bd8800e4a325be0fc36e2bf19029e399e075e836734a1f403</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2018</creationdate><topic>Acoustic coupling</topic><topic>Acoustics</topic><topic>Boundary control</topic><topic>Communications Engineering</topic><topic>Control</topic><topic>Controllability</topic><topic>Hybrid systems</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>Mechatronics</topic><topic>Networks</topic><topic>Original Article</topic><topic>Plates (structural members)</topic><topic>Robotics</topic><topic>Stability</topic><topic>Systems Theory</topic><topic>Wave equations</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Yang, Fengyan</creatorcontrib><creatorcontrib>Yao, Pengfei</creatorcontrib><creatorcontrib>Chen, Goong</creatorcontrib><collection>CrossRef</collection><collection>ProQuest Central (Corporate)</collection><collection>Computer and Information Systems Abstracts</collection><collection>Electronics & Communications Abstracts</collection><collection>ABI/INFORM Collection</collection><collection>ABI/INFORM Global (PDF only)</collection><collection>ProQuest Central (purchase pre-March 2016)</collection><collection>ABI/INFORM Global (Alumni Edition)</collection><collection>Science Database (Alumni Edition)</collection><collection>Computing Database (Alumni Edition)</collection><collection>ProQuest Pharma Collection</collection><collection>Technology Research Database</collection><collection>ProQuest SciTech Collection</collection><collection>ProQuest Technology Collection</collection><collection>ProQuest Central (Alumni) (purchase pre-March 2016)</collection><collection>ABI/INFORM Collection (Alumni Edition)</collection><collection>Materials Science & Engineering Collection</collection><collection>ProQuest Central (Alumni Edition)</collection><collection>ProQuest Central UK/Ireland</collection><collection>Advanced Technologies & Aerospace Collection</collection><collection>ProQuest Central Essentials</collection><collection>ProQuest Central</collection><collection>Business Premium Collection</collection><collection>Technology Collection</collection><collection>ProQuest One Community College</collection><collection>ProQuest Central Korea</collection><collection>Business Premium Collection (Alumni)</collection><collection>ABI/INFORM Global (Corporate)</collection><collection>ProQuest Central Student</collection><collection>SciTech Premium Collection</collection><collection>ProQuest Computer Science Collection</collection><collection>ProQuest Business Collection (Alumni Edition)</collection><collection>ProQuest Business Collection</collection><collection>Computer Science Database</collection><collection>ABI/INFORM Professional Advanced</collection><collection>ProQuest Engineering 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>ABI/INFORM Global</collection><collection>Computing Database</collection><collection>Science Database</collection><collection>Engineering Database</collection><collection>Advanced Technologies & Aerospace Database</collection><collection>ProQuest Advanced Technologies & Aerospace Collection</collection><collection>ProQuest One Business</collection><collection>ProQuest One Business (Alumni)</collection><collection>ProQuest One Academic Eastern Edition (DO NOT USE)</collection><collection>ProQuest One Academic</collection><collection>ProQuest One Academic UKI Edition</collection><collection>Engineering Collection</collection><collection>ABI/INFORM Collection China</collection><collection>ProQuest Central Basic</collection><collection>DELNET Engineering & Technology Collection</collection><jtitle>Mathematics of control, signals, and systems</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Yang, Fengyan</au><au>Yao, Pengfei</au><au>Chen, Goong</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Boundary controllability of structural acoustic systems with variable coefficients and curved walls</atitle><jtitle>Mathematics of control, signals, and systems</jtitle><stitle>Math. Control Signals Syst</stitle><date>2018-03-01</date><risdate>2018</risdate><volume>30</volume><issue>1</issue><spage>1</spage><epage>28</epage><pages>1-28</pages><artnum>5</artnum><issn>0932-4194</issn><eissn>1435-568X</eissn><abstract>This paper studies a structural acoustic model consisting of an interior acoustic wave equation with variable coefficients and a coupled Kirchhoff plate equation with a curved middle surface. By the Riemannian geometry approach and the multiplier technique, we establish exact controllability of the hybrid system under verifiable assumptions on the geometry of the interior domain and the interface boundary with two controls: One is a Neumann boundary control exerted on the wave equation, and the other acts on the interior of the plate equation. Furthermore, if the control for the plate equation is active alone, we prove that the hybrid system with partial Robin boundary condition of the wave equation is exactly controllable with the plate component and approximately controllable with the wave component.</abstract><cop>London</cop><pub>Springer London</pub><doi>10.1007/s00498-018-0211-7</doi><tpages>28</tpages><orcidid>https://orcid.org/0000-0002-2164-5217</orcidid></addata></record> |
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| ispartof | Mathematics of control, signals, and systems, 2018-03, Vol.30 (1), p.1-28, Article 5 |
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| subjects | Acoustic coupling Acoustics Boundary control Communications Engineering Control Controllability Hybrid systems Mathematics Mathematics and Statistics Mechatronics Networks Original Article Plates (structural members) Robotics Stability Systems Theory Wave equations |
| title | Boundary controllability of structural acoustic systems with variable coefficients and curved walls |
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