Optimization of Boundary Value Problems for Certain Higher-Order Differential Inclusions
The present paper studies a new class of problems of optimal control theory with special differential inclusions described by higher-order linear differential operators (HLDOs). There arises a rather complicated problem with simultaneous determination of the HLDOs and a Mayer functional depending of...
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| Veröffentlicht in: | Journal of dynamical and control systems 2019, Vol.25 (1), p.17-27 |
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| container_title | Journal of dynamical and control systems |
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| creator | Mahmudov, Elimhan N. |
| description | The present paper studies a new class of problems of optimal control theory with special differential inclusions described by higher-order linear differential operators (HLDOs). There arises a rather complicated problem with simultaneous determination of the HLDOs and a Mayer functional depending of high-order derivatives of searched functions. The sufficient conditions, containing both the Euler-Lagrange and Hamiltonian type inclusions and “transversality” conditions at the endpoints
t
= − 1, 0 and
t
= 1 are derived. One of the key features in the proof of sufficient conditions is the notion of locally adjoint mappings. Then, we demonstrate how these conditions can be transformed into Pontryagin’s maximum principle in some particular cases. |
| doi_str_mv | 10.1007/s10883-017-9392-5 |
| format | Article |
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t
= − 1, 0 and
t
= 1 are derived. One of the key features in the proof of sufficient conditions is the notion of locally adjoint mappings. Then, we demonstrate how these conditions can be transformed into Pontryagin’s maximum principle in some particular cases.</description><identifier>ISSN: 1079-2724</identifier><identifier>EISSN: 1573-8698</identifier><identifier>DOI: 10.1007/s10883-017-9392-5</identifier><language>eng</language><publisher>New York: Springer US</publisher><subject>Boundary value problems ; Calculus of Variations and Optimal Control; Optimization ; Control ; Control theory ; Differential equations ; Dynamical Systems ; Dynamical Systems and Ergodic Theory ; Economic models ; Functionals ; Inclusions ; Mathematics ; Mathematics and Statistics ; Maximum principle ; Operators (mathematics) ; Optimal control ; Systems Theory ; Vibration</subject><ispartof>Journal of dynamical and control systems, 2019, Vol.25 (1), p.17-27</ispartof><rights>Springer Science+Business Media, LLC, part of Springer Nature 2018</rights><rights>Copyright Springer Science & Business Media 2019</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><cites>FETCH-LOGICAL-c268t-8ed3950134794ced6df8f9b1f81e553943d8d37f95f77fa5f7d54eb5f9ba95e13</cites><orcidid>0000-0003-2879-6154</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/s10883-017-9392-5$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/s10883-017-9392-5$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>314,776,780,27901,27902,41464,42533,51294</link.rule.ids></links><search><creatorcontrib>Mahmudov, Elimhan N.</creatorcontrib><title>Optimization of Boundary Value Problems for Certain Higher-Order Differential Inclusions</title><title>Journal of dynamical and control systems</title><addtitle>J Dyn Control Syst</addtitle><description>The present paper studies a new class of problems of optimal control theory with special differential inclusions described by higher-order linear differential operators (HLDOs). There arises a rather complicated problem with simultaneous determination of the HLDOs and a Mayer functional depending of high-order derivatives of searched functions. The sufficient conditions, containing both the Euler-Lagrange and Hamiltonian type inclusions and “transversality” conditions at the endpoints
t
= − 1, 0 and
t
= 1 are derived. One of the key features in the proof of sufficient conditions is the notion of locally adjoint mappings. Then, we demonstrate how these conditions can be transformed into Pontryagin’s maximum principle in some particular cases.</description><subject>Boundary value problems</subject><subject>Calculus of Variations and Optimal Control; Optimization</subject><subject>Control</subject><subject>Control theory</subject><subject>Differential equations</subject><subject>Dynamical Systems</subject><subject>Dynamical Systems and Ergodic Theory</subject><subject>Economic models</subject><subject>Functionals</subject><subject>Inclusions</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Maximum principle</subject><subject>Operators (mathematics)</subject><subject>Optimal control</subject><subject>Systems Theory</subject><subject>Vibration</subject><issn>1079-2724</issn><issn>1573-8698</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2019</creationdate><recordtype>article</recordtype><recordid>eNp1kM1OAyEURonRxFp9AHckrlEYhgGWWn_apEldqHFH6HCp00yHCjMLfXppxsSVGy6L83039yB0yeg1o1TeJEaV4oQySTTXBRFHaMKE5ERVWh3nP5WaFLIoT9FZSltKqVZcTdD7at83u-bb9k3ocPD4Lgyds_ELv9l2APwcw7qFXcI-RDyD2Numw_Nm8wGRrKKDiO8b7yFC1ze2xYuuboeUq9I5OvG2TXDxO6fo9fHhZTYny9XTYna7JHVRqZ4ocFwLyngpdVmDq5xXXq-ZVwyE4LrkTjkuvRZeSm_z60QJa5EZqwUwPkVXY-8-hs8BUm-2YYhdXmkKVhWCac4PFBupOoaUInizj80un2kYNQeBZhRoskBzEGhEzhRjJmW220D8a_4_9AOqBHQE</recordid><startdate>2019</startdate><enddate>2019</enddate><creator>Mahmudov, Elimhan N.</creator><general>Springer US</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope><orcidid>https://orcid.org/0000-0003-2879-6154</orcidid></search><sort><creationdate>2019</creationdate><title>Optimization of Boundary Value Problems for Certain Higher-Order Differential Inclusions</title><author>Mahmudov, Elimhan N.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c268t-8ed3950134794ced6df8f9b1f81e553943d8d37f95f77fa5f7d54eb5f9ba95e13</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2019</creationdate><topic>Boundary value problems</topic><topic>Calculus of Variations and Optimal Control; Optimization</topic><topic>Control</topic><topic>Control theory</topic><topic>Differential equations</topic><topic>Dynamical Systems</topic><topic>Dynamical Systems and Ergodic Theory</topic><topic>Economic models</topic><topic>Functionals</topic><topic>Inclusions</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>Maximum principle</topic><topic>Operators (mathematics)</topic><topic>Optimal control</topic><topic>Systems Theory</topic><topic>Vibration</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Mahmudov, Elimhan N.</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>Mahmudov, Elimhan N.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Optimization of Boundary Value Problems for Certain Higher-Order Differential Inclusions</atitle><jtitle>Journal of dynamical and control systems</jtitle><stitle>J Dyn Control Syst</stitle><date>2019</date><risdate>2019</risdate><volume>25</volume><issue>1</issue><spage>17</spage><epage>27</epage><pages>17-27</pages><issn>1079-2724</issn><eissn>1573-8698</eissn><abstract>The present paper studies a new class of problems of optimal control theory with special differential inclusions described by higher-order linear differential operators (HLDOs). There arises a rather complicated problem with simultaneous determination of the HLDOs and a Mayer functional depending of high-order derivatives of searched functions. The sufficient conditions, containing both the Euler-Lagrange and Hamiltonian type inclusions and “transversality” conditions at the endpoints
t
= − 1, 0 and
t
= 1 are derived. One of the key features in the proof of sufficient conditions is the notion of locally adjoint mappings. Then, we demonstrate how these conditions can be transformed into Pontryagin’s maximum principle in some particular cases.</abstract><cop>New York</cop><pub>Springer US</pub><doi>10.1007/s10883-017-9392-5</doi><tpages>11</tpages><orcidid>https://orcid.org/0000-0003-2879-6154</orcidid></addata></record> |
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| language | eng |
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| subjects | Boundary value problems Calculus of Variations and Optimal Control Optimization Control Control theory Differential equations Dynamical Systems Dynamical Systems and Ergodic Theory Economic models Functionals Inclusions Mathematics Mathematics and Statistics Maximum principle Operators (mathematics) Optimal control Systems Theory Vibration |
| title | Optimization of Boundary Value Problems for Certain Higher-Order Differential Inclusions |
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