Exploiting Characteristics in Stationary Action Problems
Connections between the principle of least action and optimal control are explored with a view to describing the trajectories of energy conserving systems, subject to temporal boundary conditions, as solutions of corresponding systems of characteristics equations on arbitrary time horizons. Motivate...
Gespeichert in:
| Veröffentlicht in: | Applied mathematics & optimization 2021-12, Vol.84 (Suppl 1), p.733-765 |
|---|---|
| Hauptverfasser: | , , , |
| Format: | Artikel |
| Sprache: | eng |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| container_end_page | 765 |
|---|---|
| container_issue | Suppl 1 |
| container_start_page | 733 |
| container_title | Applied mathematics & optimization |
| container_volume | 84 |
| creator | Basco, Vincenzo Dower, Peter M. McEneaney, William M. Yegorov, Ivan |
| description | Connections between the principle of least action and optimal control are explored with a view to describing the trajectories of energy conserving systems, subject to temporal boundary conditions, as solutions of corresponding systems of characteristics equations on arbitrary time horizons. Motivated by the relaxation of least action to stationary action for longer time horizons, due to loss of convexity of the action functional, a corresponding relaxation of optimal control problems to stationary control problems is considered. In characterizing the attendant stationary controls, corresponding to generalized velocity trajectories, an auxiliary stationary control problem is posed with respect to the characteristic system of interest. Using this auxiliary problem, it is shown that the controls rendering the action functional stationary on arbitrary time horizons have a state feedback representation, via a verification theorem, that is consistent with the optimal control on short time horizons. An example is provided to illustrate application via a simple mass-spring system. |
| doi_str_mv | 10.1007/s00245-021-09784-6 |
| format | Article |
| fullrecord | <record><control><sourceid>proquest_webof</sourceid><recordid>TN_cdi_webofscience_primary_000670166700001</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>2575154955</sourcerecordid><originalsourceid>FETCH-LOGICAL-c319t-2dfaf4507aad4828b5189197f7b98eee9ee58045e5f783e4c8a7bda1a83f7b0b3</originalsourceid><addsrcrecordid>eNqNkMtKAzEUhoMoWC8v4GrApYyeTO7LMtQLCArqOmTSTE2pk5qkqG9v6ojuxCySs_j-nHM-hE4wnGMAcZEAGspqaHANSkha8x00wZQ0NXDgu2gCoFhNOeb76CClJRSecDJBcva-XgWf_bCo2mcTjc0u-pS9TZUfqodssg-DiR_V1G6r6j6GbuVe0hHa680quePv9xA9Xc4e2-v69u7qpp3e1pZgletm3pueMhDGzKlsZMewVFiJXnRKOueUc0wCZY71QhJHrTSimxtsJCkIdOQQnY7_rmN43biU9TJs4lBa6oYJhhlVjBWqGSkbQ0rR9Xod_UsZW2PQW0N6NKSLIf1lSPMSkmPozXWhT9a7wbqfYFHEBWBernJw60cVbdgMuUTP_h8tNBnpVIhh4eLvDn-M9wn3Pomf</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>2575154955</pqid></control><display><type>article</type><title>Exploiting Characteristics in Stationary Action Problems</title><source>Business Source Complete</source><source>SpringerNature Journals</source><source>Web of Science - Science Citation Index Expanded - 2021<img src="https://exlibris-pub.s3.amazonaws.com/fromwos-v2.jpg" /></source><creator>Basco, Vincenzo ; Dower, Peter M. ; McEneaney, William M. ; Yegorov, Ivan</creator><creatorcontrib>Basco, Vincenzo ; Dower, Peter M. ; McEneaney, William M. ; Yegorov, Ivan</creatorcontrib><description>Connections between the principle of least action and optimal control are explored with a view to describing the trajectories of energy conserving systems, subject to temporal boundary conditions, as solutions of corresponding systems of characteristics equations on arbitrary time horizons. Motivated by the relaxation of least action to stationary action for longer time horizons, due to loss of convexity of the action functional, a corresponding relaxation of optimal control problems to stationary control problems is considered. In characterizing the attendant stationary controls, corresponding to generalized velocity trajectories, an auxiliary stationary control problem is posed with respect to the characteristic system of interest. Using this auxiliary problem, it is shown that the controls rendering the action functional stationary on arbitrary time horizons have a state feedback representation, via a verification theorem, that is consistent with the optimal control on short time horizons. An example is provided to illustrate application via a simple mass-spring system.</description><identifier>ISSN: 0095-4616</identifier><identifier>EISSN: 1432-0606</identifier><identifier>DOI: 10.1007/s00245-021-09784-6</identifier><language>eng</language><publisher>New York: Springer US</publisher><subject>Applied mathematics ; Boundary conditions ; Calculus of Variations and Optimal Control; Optimization ; Control ; Convexity ; Hilbert space ; Mass-spring systems ; Mathematical and Computational Physics ; Mathematical functions ; Mathematical Methods in Physics ; Mathematics ; Mathematics and Statistics ; Mathematics, Applied ; Numerical and Computational Physics ; Optimal control ; Optimization ; Partial differential equations ; Physical Sciences ; Principle of least action ; Science & Technology ; Simulation ; State feedback ; Systems Theory ; Theoretical ; Trajectory control ; Velocity</subject><ispartof>Applied mathematics & optimization, 2021-12, Vol.84 (Suppl 1), p.733-765</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>true</woscitedreferencessubscribed><woscitedreferencescount>2</woscitedreferencescount><woscitedreferencesoriginalsourcerecordid>wos000670166700001</woscitedreferencesoriginalsourcerecordid><citedby>FETCH-LOGICAL-c319t-2dfaf4507aad4828b5189197f7b98eee9ee58045e5f783e4c8a7bda1a83f7b0b3</citedby><cites>FETCH-LOGICAL-c319t-2dfaf4507aad4828b5189197f7b98eee9ee58045e5f783e4c8a7bda1a83f7b0b3</cites><orcidid>0000-0002-9791-7776 ; 0000-0002-8873-8469</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/s00245-021-09784-6$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/s00245-021-09784-6$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>315,781,785,27929,27930,39263,41493,42562,51324</link.rule.ids></links><search><creatorcontrib>Basco, Vincenzo</creatorcontrib><creatorcontrib>Dower, Peter M.</creatorcontrib><creatorcontrib>McEneaney, William M.</creatorcontrib><creatorcontrib>Yegorov, Ivan</creatorcontrib><title>Exploiting Characteristics in Stationary Action Problems</title><title>Applied mathematics & optimization</title><addtitle>Appl Math Optim</addtitle><addtitle>APPL MATH OPT</addtitle><description>Connections between the principle of least action and optimal control are explored with a view to describing the trajectories of energy conserving systems, subject to temporal boundary conditions, as solutions of corresponding systems of characteristics equations on arbitrary time horizons. Motivated by the relaxation of least action to stationary action for longer time horizons, due to loss of convexity of the action functional, a corresponding relaxation of optimal control problems to stationary control problems is considered. In characterizing the attendant stationary controls, corresponding to generalized velocity trajectories, an auxiliary stationary control problem is posed with respect to the characteristic system of interest. Using this auxiliary problem, it is shown that the controls rendering the action functional stationary on arbitrary time horizons have a state feedback representation, via a verification theorem, that is consistent with the optimal control on short time horizons. An example is provided to illustrate application via a simple mass-spring system.</description><subject>Applied mathematics</subject><subject>Boundary conditions</subject><subject>Calculus of Variations and Optimal Control; Optimization</subject><subject>Control</subject><subject>Convexity</subject><subject>Hilbert space</subject><subject>Mass-spring systems</subject><subject>Mathematical and Computational Physics</subject><subject>Mathematical functions</subject><subject>Mathematical Methods in Physics</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Mathematics, Applied</subject><subject>Numerical and Computational Physics</subject><subject>Optimal control</subject><subject>Optimization</subject><subject>Partial differential equations</subject><subject>Physical Sciences</subject><subject>Principle of least action</subject><subject>Science & Technology</subject><subject>Simulation</subject><subject>State feedback</subject><subject>Systems Theory</subject><subject>Theoretical</subject><subject>Trajectory control</subject><subject>Velocity</subject><issn>0095-4616</issn><issn>1432-0606</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2021</creationdate><recordtype>article</recordtype><sourceid>HGBXW</sourceid><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>eNqNkMtKAzEUhoMoWC8v4GrApYyeTO7LMtQLCArqOmTSTE2pk5qkqG9v6ojuxCySs_j-nHM-hE4wnGMAcZEAGspqaHANSkha8x00wZQ0NXDgu2gCoFhNOeb76CClJRSecDJBcva-XgWf_bCo2mcTjc0u-pS9TZUfqodssg-DiR_V1G6r6j6GbuVe0hHa680quePv9xA9Xc4e2-v69u7qpp3e1pZgletm3pueMhDGzKlsZMewVFiJXnRKOueUc0wCZY71QhJHrTSimxtsJCkIdOQQnY7_rmN43biU9TJs4lBa6oYJhhlVjBWqGSkbQ0rR9Xod_UsZW2PQW0N6NKSLIf1lSPMSkmPozXWhT9a7wbqfYFHEBWBernJw60cVbdgMuUTP_h8tNBnpVIhh4eLvDn-M9wn3Pomf</recordid><startdate>20211201</startdate><enddate>20211201</enddate><creator>Basco, Vincenzo</creator><creator>Dower, Peter M.</creator><creator>McEneaney, William M.</creator><creator>Yegorov, Ivan</creator><general>Springer US</general><general>Springer Nature</general><general>Springer Nature B.V</general><scope>BLEPL</scope><scope>DTL</scope><scope>HGBXW</scope><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/0000-0002-9791-7776</orcidid><orcidid>https://orcid.org/0000-0002-8873-8469</orcidid></search><sort><creationdate>20211201</creationdate><title>Exploiting Characteristics in Stationary Action Problems</title><author>Basco, Vincenzo ; Dower, Peter M. ; McEneaney, William M. ; Yegorov, Ivan</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c319t-2dfaf4507aad4828b5189197f7b98eee9ee58045e5f783e4c8a7bda1a83f7b0b3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2021</creationdate><topic>Applied mathematics</topic><topic>Boundary conditions</topic><topic>Calculus of Variations and Optimal Control; Optimization</topic><topic>Control</topic><topic>Convexity</topic><topic>Hilbert space</topic><topic>Mass-spring systems</topic><topic>Mathematical and Computational Physics</topic><topic>Mathematical functions</topic><topic>Mathematical Methods in Physics</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>Mathematics, Applied</topic><topic>Numerical and Computational Physics</topic><topic>Optimal control</topic><topic>Optimization</topic><topic>Partial differential equations</topic><topic>Physical Sciences</topic><topic>Principle of least action</topic><topic>Science & Technology</topic><topic>Simulation</topic><topic>State feedback</topic><topic>Systems Theory</topic><topic>Theoretical</topic><topic>Trajectory control</topic><topic>Velocity</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Basco, Vincenzo</creatorcontrib><creatorcontrib>Dower, Peter M.</creatorcontrib><creatorcontrib>McEneaney, William M.</creatorcontrib><creatorcontrib>Yegorov, Ivan</creatorcontrib><collection>Web of Science Core Collection</collection><collection>Science Citation Index Expanded</collection><collection>Web of Science - Science Citation Index Expanded - 2021</collection><collection>CrossRef</collection><collection>ProQuest Central (Corporate)</collection><collection>Access via ABI/INFORM (ProQuest)</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>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>ProQuest Central Basic</collection><jtitle>Applied mathematics & optimization</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Basco, Vincenzo</au><au>Dower, Peter M.</au><au>McEneaney, William M.</au><au>Yegorov, Ivan</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Exploiting Characteristics in Stationary Action Problems</atitle><jtitle>Applied mathematics & optimization</jtitle><stitle>Appl Math Optim</stitle><stitle>APPL MATH OPT</stitle><date>2021-12-01</date><risdate>2021</risdate><volume>84</volume><issue>Suppl 1</issue><spage>733</spage><epage>765</epage><pages>733-765</pages><issn>0095-4616</issn><eissn>1432-0606</eissn><abstract>Connections between the principle of least action and optimal control are explored with a view to describing the trajectories of energy conserving systems, subject to temporal boundary conditions, as solutions of corresponding systems of characteristics equations on arbitrary time horizons. Motivated by the relaxation of least action to stationary action for longer time horizons, due to loss of convexity of the action functional, a corresponding relaxation of optimal control problems to stationary control problems is considered. In characterizing the attendant stationary controls, corresponding to generalized velocity trajectories, an auxiliary stationary control problem is posed with respect to the characteristic system of interest. Using this auxiliary problem, it is shown that the controls rendering the action functional stationary on arbitrary time horizons have a state feedback representation, via a verification theorem, that is consistent with the optimal control on short time horizons. An example is provided to illustrate application via a simple mass-spring system.</abstract><cop>New York</cop><pub>Springer US</pub><doi>10.1007/s00245-021-09784-6</doi><tpages>33</tpages><orcidid>https://orcid.org/0000-0002-9791-7776</orcidid><orcidid>https://orcid.org/0000-0002-8873-8469</orcidid></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 0095-4616 |
| ispartof | Applied mathematics & optimization, 2021-12, Vol.84 (Suppl 1), p.733-765 |
| issn | 0095-4616 1432-0606 |
| language | eng |
| recordid | cdi_webofscience_primary_000670166700001 |
| source | Business Source Complete; SpringerNature Journals; Web of Science - Science Citation Index Expanded - 2021<img src="https://exlibris-pub.s3.amazonaws.com/fromwos-v2.jpg" /> |
| subjects | Applied mathematics Boundary conditions Calculus of Variations and Optimal Control Optimization Control Convexity Hilbert space Mass-spring systems Mathematical and Computational Physics Mathematical functions Mathematical Methods in Physics Mathematics Mathematics and Statistics Mathematics, Applied Numerical and Computational Physics Optimal control Optimization Partial differential equations Physical Sciences Principle of least action Science & Technology Simulation State feedback Systems Theory Theoretical Trajectory control Velocity |
| title | Exploiting Characteristics in Stationary Action Problems |
| url | https://sfx.bib-bvb.de/sfx_tum?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2024-12-11T21%3A58%3A28IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-proquest_webof&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=Exploiting%20Characteristics%20in%20Stationary%20Action%20Problems&rft.jtitle=Applied%20mathematics%20&%20optimization&rft.au=Basco,%20Vincenzo&rft.date=2021-12-01&rft.volume=84&rft.issue=Suppl%201&rft.spage=733&rft.epage=765&rft.pages=733-765&rft.issn=0095-4616&rft.eissn=1432-0606&rft_id=info:doi/10.1007/s00245-021-09784-6&rft_dat=%3Cproquest_webof%3E2575154955%3C/proquest_webof%3E%3Curl%3E%3C/url%3E&disable_directlink=true&sfx.directlink=off&sfx.report_link=0&rft_id=info:oai/&rft_pqid=2575154955&rft_id=info:pmid/&rfr_iscdi=true |