Optimal control and optimality condition of the Camassa–Holm equation
This paper is devoted to the optimal distributed control problem described by Camassa–Holm equation. We firstly investigate the existence and uniqueness of weak solution for the controlled system with appropriate initial value and boundary condition. By contrast with our previous result, the proof w...
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| Veröffentlicht in: | European journal of control 2017-07, Vol.36, p.18-29 |
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| container_title | European journal of control |
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| creator | Shen, Chunyu Tian, Lixin |
| description | This paper is devoted to the optimal distributed control problem described by Camassa–Holm equation. We firstly investigate the existence and uniqueness of weak solution for the controlled system with appropriate initial value and boundary condition. By contrast with our previous result, the proof without considering viscous coefficient is a bigger improvement. Secondly, based on the well-posedness result, we find a unique optimal control for the controlled system with the quadratic cost functional. Moreover, by means of the optimal control theory, we establish the sufficient and necessary optimality condition of an optimal control, which is another major novelty of this paper. Finally, we also present the optimality conditions corresponding to two physical meaningful distributive observation cases and give an illustration about how to numerically apply the obtained results. |
| doi_str_mv | 10.1016/j.ejcon.2017.04.004 |
| format | Article |
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Finally, we also present the optimality conditions corresponding to two physical meaningful distributive observation cases and give an illustration about how to numerically apply the obtained results.</description><identifier>ISSN: 0947-3580</identifier><identifier>EISSN: 1435-5671</identifier><identifier>DOI: 10.1016/j.ejcon.2017.04.004</identifier><language>eng</language><publisher>Philadelphia: Elsevier Ltd</publisher><subject>Boundary value problems ; Camassa–Holm equation ; Coefficients ; Control systems ; Control theory ; Design optimization ; Economic models ; Existence and uniqueness ; Fluid dynamics ; Linear equations ; Mathematical analysis ; Nonlinear equations ; Optimal control ; Partial differential equations ; Queuing theory ; Sufficient and necessary optimality condition ; Uniqueness ; Weak solution</subject><ispartof>European journal of control, 2017-07, Vol.36, p.18-29</ispartof><rights>2017 European Control Association</rights><rights>Copyright Elsevier Limited 2017</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c331t-10dbc923554db78314f90bf279474d528fc9885b3d749b7110e6a80e4ffe9a063</citedby><cites>FETCH-LOGICAL-c331t-10dbc923554db78314f90bf279474d528fc9885b3d749b7110e6a80e4ffe9a063</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktohtml>$$Uhttps://www.proquest.com/docview/1911187293?pq-origsite=primo$$EHTML$$P50$$Gproquest$$H</linktohtml><link.rule.ids>314,780,784,27915,27916,64374,64378,72230</link.rule.ids></links><search><creatorcontrib>Shen, Chunyu</creatorcontrib><creatorcontrib>Tian, Lixin</creatorcontrib><title>Optimal control and optimality condition of the Camassa–Holm equation</title><title>European journal of control</title><description>This paper is devoted to the optimal distributed control problem described by Camassa–Holm equation. 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Tian, Lixin</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c331t-10dbc923554db78314f90bf279474d528fc9885b3d749b7110e6a80e4ffe9a063</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2017</creationdate><topic>Boundary value problems</topic><topic>Camassa–Holm equation</topic><topic>Coefficients</topic><topic>Control systems</topic><topic>Control theory</topic><topic>Design optimization</topic><topic>Economic models</topic><topic>Existence and uniqueness</topic><topic>Fluid dynamics</topic><topic>Linear equations</topic><topic>Mathematical analysis</topic><topic>Nonlinear equations</topic><topic>Optimal control</topic><topic>Partial differential equations</topic><topic>Queuing theory</topic><topic>Sufficient and necessary optimality condition</topic><topic>Uniqueness</topic><topic>Weak solution</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Shen, Chunyu</creatorcontrib><creatorcontrib>Tian, Lixin</creatorcontrib><collection>CrossRef</collection><collection>ProQuest Central (Corporate)</collection><collection>ProQuest Central (purchase pre-March 2016)</collection><collection>Science Database (Alumni Edition)</collection><collection>Computing Database (Alumni Edition)</collection><collection>ProQuest SciTech Collection</collection><collection>ProQuest Technology Collection</collection><collection>ProQuest Central (Alumni) (purchase pre-March 2016)</collection><collection>Materials Science & Engineering Collection</collection><collection>ProQuest Central (Alumni)</collection><collection>ProQuest Central</collection><collection>Advanced Technologies & Aerospace Database (1962 - current)</collection><collection>ProQuest Central Essentials</collection><collection>AUTh Library subscriptions: ProQuest Central</collection><collection>Technology Collection</collection><collection>ProQuest One Community College</collection><collection>ProQuest Central</collection><collection>ProQuest Central Student</collection><collection>SciTech Premium Collection</collection><collection>ProQuest Computer Science Collection</collection><collection>Computer Science Database</collection><collection>ProQuest Engineering Collection</collection><collection>Computing Database</collection><collection>ProQuest Science Journals</collection><collection>ProQuest Engineering Database</collection><collection>ProQuest Advanced Technologies & Aerospace Database</collection><collection>ProQuest Advanced Technologies & Aerospace Collection</collection><collection>ProQuest One Academic Eastern Edition (DO NOT USE)</collection><collection>ProQuest One Academic</collection><collection>ProQuest One Academic UKI Edition</collection><collection>ProQuest Central China</collection><collection>Engineering Collection</collection><collection>ProQuest Central Basic</collection><jtitle>European journal of control</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Shen, Chunyu</au><au>Tian, Lixin</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Optimal control and optimality condition of the Camassa–Holm equation</atitle><jtitle>European journal of control</jtitle><date>2017-07-01</date><risdate>2017</risdate><volume>36</volume><spage>18</spage><epage>29</epage><pages>18-29</pages><issn>0947-3580</issn><eissn>1435-5671</eissn><abstract>This paper is devoted to the optimal distributed control problem described by Camassa–Holm equation. We firstly investigate the existence and uniqueness of weak solution for the controlled system with appropriate initial value and boundary condition. By contrast with our previous result, the proof without considering viscous coefficient is a bigger improvement. Secondly, based on the well-posedness result, we find a unique optimal control for the controlled system with the quadratic cost functional. Moreover, by means of the optimal control theory, we establish the sufficient and necessary optimality condition of an optimal control, which is another major novelty of this paper. Finally, we also present the optimality conditions corresponding to two physical meaningful distributive observation cases and give an illustration about how to numerically apply the obtained results.</abstract><cop>Philadelphia</cop><pub>Elsevier Ltd</pub><doi>10.1016/j.ejcon.2017.04.004</doi><tpages>12</tpages></addata></record> |
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| ispartof | European journal of control, 2017-07, Vol.36, p.18-29 |
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| language | eng |
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| source | Alma/SFX Local Collection; ProQuest Central |
| subjects | Boundary value problems Camassa–Holm equation Coefficients Control systems Control theory Design optimization Economic models Existence and uniqueness Fluid dynamics Linear equations Mathematical analysis Nonlinear equations Optimal control Partial differential equations Queuing theory Sufficient and necessary optimality condition Uniqueness Weak solution |
| title | Optimal control and optimality condition of the Camassa–Holm equation |
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