Sensitivity Analysis of Optimal Control Problems Governed by Nonlinear Hilfer Fractional Evolution Inclusions
This article studies sensitivity properties of optimal control problems that are governed by nonlinear Hilfer fractional evolution inclusions (NHFEIs) in Hilbert spaces, where the initial state ξ is not the classical Cauchy, but is the Riemann–Liouville integral. First, we obtain the nonemptiness an...
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| Veröffentlicht in: | Applied mathematics & optimization 2021-12, Vol.84 (3), p.3045-3082 |
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| container_title | Applied mathematics & optimization |
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| creator | Jiang, Yirong Zhang, Qiongfen Chen, An Wei, Zhouchao |
| description | This article studies sensitivity properties of optimal control problems that are governed by nonlinear Hilfer fractional evolution inclusions (NHFEIs) in Hilbert spaces, where the initial state
ξ
is not the classical Cauchy, but is the Riemann–Liouville integral. First, we obtain the nonemptiness and the compactness properties of mild solution sets
S
(
ξ
)
for NHFEIs, and also establish an extension Filippov’s theorem. Then we obtain the continuity and upper semicontinuity of optimal control problems connected with NHFEIs depending on a initial state
ξ
as well as a parameter
λ
. Finally, An illustrating example is given. |
| doi_str_mv | 10.1007/s00245-020-09739-3 |
| format | Article |
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ξ
is not the classical Cauchy, but is the Riemann–Liouville integral. First, we obtain the nonemptiness and the compactness properties of mild solution sets
S
(
ξ
)
for NHFEIs, and also establish an extension Filippov’s theorem. Then we obtain the continuity and upper semicontinuity of optimal control problems connected with NHFEIs depending on a initial state
ξ
as well as a parameter
λ
. Finally, An illustrating example is given.</description><identifier>ISSN: 0095-4616</identifier><identifier>EISSN: 1432-0606</identifier><identifier>DOI: 10.1007/s00245-020-09739-3</identifier><language>eng</language><publisher>New York: Springer US</publisher><subject>Applied mathematics ; Banach spaces ; Calculus of Variations and Optimal Control; Optimization ; Control ; Control theory ; Evolution ; Hilbert space ; Inclusions ; Mathematical and Computational Physics ; Mathematical Methods in Physics ; Mathematics ; Mathematics and Statistics ; Numerical and Computational Physics ; Optimal control ; Optimization ; Science ; Sensitivity analysis ; Simulation ; Systems Theory ; Theoretical</subject><ispartof>Applied mathematics & optimization, 2021-12, Vol.84 (3), p.3045-3082</ispartof><rights>The Author(s), under exclusive licence to Springer Science+Business Media, LLC part of Springer Nature 2021</rights><rights>The Author(s), under exclusive licence to Springer Science+Business Media, LLC part of Springer Nature 2021.</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c319t-e963e76070deb1b9e6e6979ca1dfcb4e74736022399a9bc5ace6fc42adcd63813</citedby><cites>FETCH-LOGICAL-c319t-e963e76070deb1b9e6e6979ca1dfcb4e74736022399a9bc5ace6fc42adcd63813</cites><orcidid>0000-0001-6981-748X</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/s00245-020-09739-3$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/s00245-020-09739-3$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>314,780,784,27923,27924,41487,42556,51318</link.rule.ids></links><search><creatorcontrib>Jiang, Yirong</creatorcontrib><creatorcontrib>Zhang, Qiongfen</creatorcontrib><creatorcontrib>Chen, An</creatorcontrib><creatorcontrib>Wei, Zhouchao</creatorcontrib><title>Sensitivity Analysis of Optimal Control Problems Governed by Nonlinear Hilfer Fractional Evolution Inclusions</title><title>Applied mathematics & optimization</title><addtitle>Appl Math Optim</addtitle><description>This article studies sensitivity properties of optimal control problems that are governed by nonlinear Hilfer fractional evolution inclusions (NHFEIs) in Hilbert spaces, where the initial state
ξ
is not the classical Cauchy, but is the Riemann–Liouville integral. First, we obtain the nonemptiness and the compactness properties of mild solution sets
S
(
ξ
)
for NHFEIs, and also establish an extension Filippov’s theorem. Then we obtain the continuity and upper semicontinuity of optimal control problems connected with NHFEIs depending on a initial state
ξ
as well as a parameter
λ
. Finally, An illustrating example is given.</description><subject>Applied mathematics</subject><subject>Banach spaces</subject><subject>Calculus of Variations and Optimal Control; Optimization</subject><subject>Control</subject><subject>Control theory</subject><subject>Evolution</subject><subject>Hilbert space</subject><subject>Inclusions</subject><subject>Mathematical and Computational Physics</subject><subject>Mathematical Methods in Physics</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Numerical and Computational Physics</subject><subject>Optimal control</subject><subject>Optimization</subject><subject>Science</subject><subject>Sensitivity analysis</subject><subject>Simulation</subject><subject>Systems Theory</subject><subject>Theoretical</subject><issn>0095-4616</issn><issn>1432-0606</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2021</creationdate><recordtype>article</recordtype><sourceid>8G5</sourceid><sourceid>ABUWG</sourceid><sourceid>AFKRA</sourceid><sourceid>AZQEC</sourceid><sourceid>BENPR</sourceid><sourceid>CCPQU</sourceid><sourceid>DWQXO</sourceid><sourceid>GNUQQ</sourceid><sourceid>GUQSH</sourceid><sourceid>M2O</sourceid><recordid>eNp9kE1LAzEQhoMoWKt_wFPA8-rko9nmWEq_QKygnkM2Oytb0k1NtoX-e1MrePM0c3jel5mHkHsGjwygfEoAXI4K4FCALoUuxAUZMCl4AQrUJRkA6FEhFVPX5CalDWReKDEg2zfsUtu3h7Y_0kln_TG1iYaGrnd9u7WeTkPXx-DpawyVx22ii3DA2GFNqyN9CZ1vO7SRLlvfYKTzaF3fhtxDZ4fg96edrjrn9ylv6ZZcNdYnvPudQ_Ixn71Pl8XzerGaTp4LJ5juC9RKYKmghBorVmlUqHSpnWV14yqJpSyFAs6F1lZXbmQdqsZJbmtXKzFmYkgezr27GL72mHqzCfuYr0qGj9RYaCklzxQ_Uy6GlCI2Zhfzz_FoGJiTVnPWarJW86PViBwS51DKcPeJ8a_6n9Q3APB85A</recordid><startdate>20211201</startdate><enddate>20211201</enddate><creator>Jiang, Yirong</creator><creator>Zhang, Qiongfen</creator><creator>Chen, An</creator><creator>Wei, Zhouchao</creator><general>Springer US</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope><scope>3V.</scope><scope>7WY</scope><scope>7WZ</scope><scope>7XB</scope><scope>87Z</scope><scope>88I</scope><scope>8AO</scope><scope>8FE</scope><scope>8FG</scope><scope>8FK</scope><scope>8FL</scope><scope>8G5</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>GUQSH</scope><scope>HCIFZ</scope><scope>JQ2</scope><scope>K60</scope><scope>K6~</scope><scope>K7-</scope><scope>L.-</scope><scope>L6V</scope><scope>M0C</scope><scope>M2O</scope><scope>M2P</scope><scope>M7S</scope><scope>MBDVC</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>Q9U</scope><orcidid>https://orcid.org/0000-0001-6981-748X</orcidid></search><sort><creationdate>20211201</creationdate><title>Sensitivity Analysis of Optimal Control Problems Governed by Nonlinear Hilfer Fractional Evolution Inclusions</title><author>Jiang, Yirong ; Zhang, Qiongfen ; Chen, An ; Wei, Zhouchao</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c319t-e963e76070deb1b9e6e6979ca1dfcb4e74736022399a9bc5ace6fc42adcd63813</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2021</creationdate><topic>Applied mathematics</topic><topic>Banach spaces</topic><topic>Calculus of Variations and Optimal Control; Optimization</topic><topic>Control</topic><topic>Control theory</topic><topic>Evolution</topic><topic>Hilbert space</topic><topic>Inclusions</topic><topic>Mathematical and Computational Physics</topic><topic>Mathematical Methods in Physics</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>Numerical and Computational Physics</topic><topic>Optimal control</topic><topic>Optimization</topic><topic>Science</topic><topic>Sensitivity analysis</topic><topic>Simulation</topic><topic>Systems Theory</topic><topic>Theoretical</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Jiang, Yirong</creatorcontrib><creatorcontrib>Zhang, Qiongfen</creatorcontrib><creatorcontrib>Chen, An</creatorcontrib><creatorcontrib>Wei, Zhouchao</creatorcontrib><collection>CrossRef</collection><collection>ProQuest Central (Corporate)</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>ProQuest Pharma Collection</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>Research Library (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>Research Library Prep</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>ABI/INFORM Global</collection><collection>Research Library</collection><collection>Science Database</collection><collection>Engineering Database</collection><collection>Research Library (Corporate)</collection><collection>Advanced Technologies & Aerospace Database</collection><collection>ProQuest Advanced Technologies & Aerospace Collection</collection><collection>One Business (ProQuest)</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>ProQuest Central Basic</collection><jtitle>Applied mathematics & optimization</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Jiang, Yirong</au><au>Zhang, Qiongfen</au><au>Chen, An</au><au>Wei, Zhouchao</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Sensitivity Analysis of Optimal Control Problems Governed by Nonlinear Hilfer Fractional Evolution Inclusions</atitle><jtitle>Applied mathematics & optimization</jtitle><stitle>Appl Math Optim</stitle><date>2021-12-01</date><risdate>2021</risdate><volume>84</volume><issue>3</issue><spage>3045</spage><epage>3082</epage><pages>3045-3082</pages><issn>0095-4616</issn><eissn>1432-0606</eissn><abstract>This article studies sensitivity properties of optimal control problems that are governed by nonlinear Hilfer fractional evolution inclusions (NHFEIs) in Hilbert spaces, where the initial state
ξ
is not the classical Cauchy, but is the Riemann–Liouville integral. First, we obtain the nonemptiness and the compactness properties of mild solution sets
S
(
ξ
)
for NHFEIs, and also establish an extension Filippov’s theorem. Then we obtain the continuity and upper semicontinuity of optimal control problems connected with NHFEIs depending on a initial state
ξ
as well as a parameter
λ
. Finally, An illustrating example is given.</abstract><cop>New York</cop><pub>Springer US</pub><doi>10.1007/s00245-020-09739-3</doi><tpages>38</tpages><orcidid>https://orcid.org/0000-0001-6981-748X</orcidid></addata></record> |
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| subjects | Applied mathematics Banach spaces Calculus of Variations and Optimal Control Optimization Control Control theory Evolution Hilbert space Inclusions Mathematical and Computational Physics Mathematical Methods in Physics Mathematics Mathematics and Statistics Numerical and Computational Physics Optimal control Optimization Science Sensitivity analysis Simulation Systems Theory Theoretical |
| title | Sensitivity Analysis of Optimal Control Problems Governed by Nonlinear Hilfer Fractional Evolution Inclusions |
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