Riccati Equations for Stable Well-Posed Linear Systems: The Generic Case
Under the generic assumption that zero is in the resolvent set of the generator, we show that the optimal control problem for a stable well-posed linear system is equivalent to a control problem for its reciprocal system which has bounded generating operators. Consequently, the operator X that defin...
Gespeichert in:
| Veröffentlicht in: | SIAM journal on control and optimization 2003-01, Vol.42 (5), p.1681-1702 |
|---|---|
| 1. Verfasser: | |
| Format: | Artikel |
| Sprache: | eng |
| Online-Zugang: | Volltext |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| container_end_page | 1702 |
|---|---|
| container_issue | 5 |
| container_start_page | 1681 |
| container_title | SIAM journal on control and optimization |
| container_volume | 42 |
| creator | Curtain, Ruth F. |
| description | Under the generic assumption that zero is in the resolvent set of the generator, we show that the optimal control problem for a stable well-posed linear system is equivalent to a control problem for its reciprocal system which has bounded generating operators. Consequently, the operator X that defines the optimal cost satisfies a Riccati equation with bounded operators. Previous results needed various regularity assumptions to obtain X as a solution to a Riccati equation resembling that in the finite-dimensional theory. |
| doi_str_mv | 10.1137/S0363012901399362 |
| format | Article |
| fullrecord | <record><control><sourceid>proquest_cross</sourceid><recordid>TN_cdi_proquest_journals_925798934</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>2600433481</sourcerecordid><originalsourceid>FETCH-LOGICAL-c270t-5557e2176ca8b79763db2afd9152066b7cc6850ce7d125e61c7a0e7efbe67ddc3</originalsourceid><addsrcrecordid>eNplkEFLwzAYhoMoOKc_wFvwXs2XNPkabzLmJhQUN_FY0vQrdnTtlnSH_Xs75s3Tc3he3hdexu5BPAIofFoJZZQAaQUoa5WRF2wCwuoEQWWXbHLSyclfs5sYN0JAmkI6YcvPxns3NHy-P4zou8jrPvDV4MqW-De1bfLRR6p43nTkRnGMA23jM1__EF9QR6HxfOYi3bKr2rWR7v44ZV-v8_VsmeTvi7fZS554iWJItNZIEtB4l5Vo0aiqlK6uLGgpjCnRe5Np4QkrkJoMeHSCkOqSDFaVV1P2cO7dhX5_oDgUm_4QunGysFKjzaxKxxCcQz70MQaqi11oti4cCxDF6a_i31_qF0hpXBk</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>925798934</pqid></control><display><type>article</type><title>Riccati Equations for Stable Well-Posed Linear Systems: The Generic Case</title><source>SIAM Journals Online</source><source>Business Source Complete</source><creator>Curtain, Ruth F.</creator><creatorcontrib>Curtain, Ruth F.</creatorcontrib><description>Under the generic assumption that zero is in the resolvent set of the generator, we show that the optimal control problem for a stable well-posed linear system is equivalent to a control problem for its reciprocal system which has bounded generating operators. Consequently, the operator X that defines the optimal cost satisfies a Riccati equation with bounded operators. Previous results needed various regularity assumptions to obtain X as a solution to a Riccati equation resembling that in the finite-dimensional theory.</description><identifier>ISSN: 0363-0129</identifier><identifier>EISSN: 1095-7138</identifier><identifier>DOI: 10.1137/S0363012901399362</identifier><language>eng</language><publisher>Philadelphia: Society for Industrial and Applied Mathematics</publisher><ispartof>SIAM journal on control and optimization, 2003-01, Vol.42 (5), p.1681-1702</ispartof><rights>[Copyright] © 2003 Society for Industrial and Applied Mathematics</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c270t-5557e2176ca8b79763db2afd9152066b7cc6850ce7d125e61c7a0e7efbe67ddc3</citedby><cites>FETCH-LOGICAL-c270t-5557e2176ca8b79763db2afd9152066b7cc6850ce7d125e61c7a0e7efbe67ddc3</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>314,780,784,3184,27924,27925</link.rule.ids></links><search><creatorcontrib>Curtain, Ruth F.</creatorcontrib><title>Riccati Equations for Stable Well-Posed Linear Systems: The Generic Case</title><title>SIAM journal on control and optimization</title><description>Under the generic assumption that zero is in the resolvent set of the generator, we show that the optimal control problem for a stable well-posed linear system is equivalent to a control problem for its reciprocal system which has bounded generating operators. Consequently, the operator X that defines the optimal cost satisfies a Riccati equation with bounded operators. Previous results needed various regularity assumptions to obtain X as a solution to a Riccati equation resembling that in the finite-dimensional theory.</description><issn>0363-0129</issn><issn>1095-7138</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2003</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>eNplkEFLwzAYhoMoOKc_wFvwXs2XNPkabzLmJhQUN_FY0vQrdnTtlnSH_Xs75s3Tc3he3hdexu5BPAIofFoJZZQAaQUoa5WRF2wCwuoEQWWXbHLSyclfs5sYN0JAmkI6YcvPxns3NHy-P4zou8jrPvDV4MqW-De1bfLRR6p43nTkRnGMA23jM1__EF9QR6HxfOYi3bKr2rWR7v44ZV-v8_VsmeTvi7fZS554iWJItNZIEtB4l5Vo0aiqlK6uLGgpjCnRe5Np4QkrkJoMeHSCkOqSDFaVV1P2cO7dhX5_oDgUm_4QunGysFKjzaxKxxCcQz70MQaqi11oti4cCxDF6a_i31_qF0hpXBk</recordid><startdate>200301</startdate><enddate>200301</enddate><creator>Curtain, Ruth F.</creator><general>Society for Industrial and Applied Mathematics</general><scope>AAYXX</scope><scope>CITATION</scope><scope>3V.</scope><scope>7RQ</scope><scope>7WY</scope><scope>7WZ</scope><scope>7X2</scope><scope>7XB</scope><scope>87Z</scope><scope>88A</scope><scope>88F</scope><scope>88I</scope><scope>88K</scope><scope>8AL</scope><scope>8FE</scope><scope>8FG</scope><scope>8FH</scope><scope>8FK</scope><scope>8FL</scope><scope>8G5</scope><scope>ABJCF</scope><scope>ABUWG</scope><scope>AFKRA</scope><scope>ARAPS</scope><scope>ATCPS</scope><scope>AZQEC</scope><scope>BBNVY</scope><scope>BENPR</scope><scope>BEZIV</scope><scope>BGLVJ</scope><scope>BHPHI</scope><scope>CCPQU</scope><scope>D1I</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>KB.</scope><scope>L.-</scope><scope>L6V</scope><scope>LK8</scope><scope>M0C</scope><scope>M0K</scope><scope>M0N</scope><scope>M1Q</scope><scope>M2O</scope><scope>M2P</scope><scope>M2T</scope><scope>M7P</scope><scope>M7S</scope><scope>MBDVC</scope><scope>P5Z</scope><scope>P62</scope><scope>PATMY</scope><scope>PDBOC</scope><scope>PQBIZ</scope><scope>PQBZA</scope><scope>PQEST</scope><scope>PQQKQ</scope><scope>PQUKI</scope><scope>PRINS</scope><scope>PTHSS</scope><scope>PYCSY</scope><scope>Q9U</scope><scope>U9A</scope></search><sort><creationdate>200301</creationdate><title>Riccati Equations for Stable Well-Posed Linear Systems: The Generic Case</title><author>Curtain, Ruth F.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c270t-5557e2176ca8b79763db2afd9152066b7cc6850ce7d125e61c7a0e7efbe67ddc3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2003</creationdate><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Curtain, Ruth F.</creatorcontrib><collection>CrossRef</collection><collection>ProQuest Central (Corporate)</collection><collection>Career & Technical Education Database</collection><collection>ABI/INFORM Collection</collection><collection>ABI/INFORM Global (PDF only)</collection><collection>Agricultural Science Collection</collection><collection>ProQuest Central (purchase pre-March 2016)</collection><collection>ABI/INFORM Global (Alumni Edition)</collection><collection>Biology Database (Alumni Edition)</collection><collection>Military Database (Alumni Edition)</collection><collection>Science Database (Alumni Edition)</collection><collection>Telecommunications (Alumni Edition)</collection><collection>Computing Database (Alumni Edition)</collection><collection>ProQuest SciTech Collection</collection><collection>ProQuest Technology Collection</collection><collection>ProQuest Natural Science 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>Agricultural & Environmental Science Collection</collection><collection>ProQuest Central Essentials</collection><collection>Biological Science Collection</collection><collection>ProQuest Central</collection><collection>Business Premium Collection</collection><collection>Technology Collection</collection><collection>Natural Science Collection</collection><collection>ProQuest One Community College</collection><collection>ProQuest Materials Science Collection</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>Materials Science Database</collection><collection>ABI/INFORM Professional Advanced</collection><collection>ProQuest Engineering Collection</collection><collection>ProQuest Biological Science Collection</collection><collection>ABI/INFORM Global</collection><collection>Agricultural Science Database</collection><collection>Computing Database</collection><collection>Military Database</collection><collection>Research Library</collection><collection>Science Database</collection><collection>Telecommunications Database</collection><collection>Biological 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>Environmental Science Database</collection><collection>Materials Science 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>ProQuest Central China</collection><collection>Engineering Collection</collection><collection>Environmental Science Collection</collection><collection>ProQuest Central Basic</collection><jtitle>SIAM journal on control and optimization</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Curtain, Ruth F.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Riccati Equations for Stable Well-Posed Linear Systems: The Generic Case</atitle><jtitle>SIAM journal on control and optimization</jtitle><date>2003-01</date><risdate>2003</risdate><volume>42</volume><issue>5</issue><spage>1681</spage><epage>1702</epage><pages>1681-1702</pages><issn>0363-0129</issn><eissn>1095-7138</eissn><abstract>Under the generic assumption that zero is in the resolvent set of the generator, we show that the optimal control problem for a stable well-posed linear system is equivalent to a control problem for its reciprocal system which has bounded generating operators. Consequently, the operator X that defines the optimal cost satisfies a Riccati equation with bounded operators. Previous results needed various regularity assumptions to obtain X as a solution to a Riccati equation resembling that in the finite-dimensional theory.</abstract><cop>Philadelphia</cop><pub>Society for Industrial and Applied Mathematics</pub><doi>10.1137/S0363012901399362</doi><tpages>22</tpages></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 0363-0129 |
| ispartof | SIAM journal on control and optimization, 2003-01, Vol.42 (5), p.1681-1702 |
| issn | 0363-0129 1095-7138 |
| language | eng |
| recordid | cdi_proquest_journals_925798934 |
| source | SIAM Journals Online; Business Source Complete |
| title | Riccati Equations for Stable Well-Posed Linear Systems: The Generic Case |
| url | https://sfx.bib-bvb.de/sfx_tum?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2025-01-05T11%3A27%3A47IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-proquest_cross&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=Riccati%20Equations%20for%20Stable%20Well-Posed%20Linear%20Systems:%20The%20Generic%20Case&rft.jtitle=SIAM%20journal%20on%20control%20and%20optimization&rft.au=Curtain,%20Ruth%20F.&rft.date=2003-01&rft.volume=42&rft.issue=5&rft.spage=1681&rft.epage=1702&rft.pages=1681-1702&rft.issn=0363-0129&rft.eissn=1095-7138&rft_id=info:doi/10.1137/S0363012901399362&rft_dat=%3Cproquest_cross%3E2600433481%3C/proquest_cross%3E%3Curl%3E%3C/url%3E&disable_directlink=true&sfx.directlink=off&sfx.report_link=0&rft_id=info:oai/&rft_pqid=925798934&rft_id=info:pmid/&rfr_iscdi=true |