Robust static and fixed‐order dynamic output feedback control of discrete‐time parametric uncertain Luré systems: Sequential SDP relaxation approaches
Summary Design methods are proposed for static and fixed‐order dynamic output feedback controllers for discrete‐time Luré systems with sector‐bounded nonlinearities in the presence of parametric uncertainties described by polytopes. The derived design conditions are represented in terms of bilinear...
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| Veröffentlicht in: | Optimal control applications & methods 2017-01, Vol.38 (1), p.36-58 |
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| creator | Kim, Kwang‐Ki K. Braatz, Richard D. |
| description | Summary
Design methods are proposed for static and fixed‐order dynamic output feedback controllers for discrete‐time Luré systems with sector‐bounded nonlinearities in the presence of parametric uncertainties described by polytopes. The derived design conditions are represented in terms of bilinear matrix inequalities, which are nonconvex. By using convex relaxation methods, controller design equations are derived for systems with multiple states, outputs, and nonlinearities in terms of linear matrix inequalities (LMIs) and iterative LMIs, which are associated with semidefinite programs. The proposed design methods are developed from stability conditions using parameter‐dependent Lyapunov functions, and existing iterative numerical methods are adapted to solve certain classes of nonconvex optimization problems for controller design. Several numerical examples are provided to illustrate and verify the proposed design methods. Copyright © 2016 John Wiley & Sons, Ltd. |
| doi_str_mv | 10.1002/oca.2241 |
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Design methods are proposed for static and fixed‐order dynamic output feedback controllers for discrete‐time Luré systems with sector‐bounded nonlinearities in the presence of parametric uncertainties described by polytopes. The derived design conditions are represented in terms of bilinear matrix inequalities, which are nonconvex. By using convex relaxation methods, controller design equations are derived for systems with multiple states, outputs, and nonlinearities in terms of linear matrix inequalities (LMIs) and iterative LMIs, which are associated with semidefinite programs. The proposed design methods are developed from stability conditions using parameter‐dependent Lyapunov functions, and existing iterative numerical methods are adapted to solve certain classes of nonconvex optimization problems for controller design. Several numerical examples are provided to illustrate and verify the proposed design methods. Copyright © 2016 John Wiley & Sons, Ltd.</description><identifier>ISSN: 0143-2087</identifier><identifier>EISSN: 1099-1514</identifier><identifier>DOI: 10.1002/oca.2241</identifier><identifier>CODEN: OCAMD5</identifier><language>eng</language><publisher>Glasgow: Wiley Subscription Services, Inc</publisher><subject>Control methods ; Controllers ; Design engineering ; Design parameters ; Dynamical systems ; fixed‐order dynamic output feedback control ; Luré system ; Mathematical analysis ; Nonlinear dynamics ; Nonlinearity ; parameter‐dependent Lyapunov function ; robust control ; static output feedback control</subject><ispartof>Optimal control applications & methods, 2017-01, Vol.38 (1), p.36-58</ispartof><rights>Copyright © 2016 John Wiley & Sons, Ltd.</rights><rights>Copyright © 2017 John Wiley & Sons, Ltd.</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c3261-e6d2d7f8e0d404b30f89923d7f859b55d7834b0342c424d6392954930a1e2dd73</citedby><cites>FETCH-LOGICAL-c3261-e6d2d7f8e0d404b30f89923d7f859b55d7834b0342c424d6392954930a1e2dd73</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://onlinelibrary.wiley.com/doi/pdf/10.1002%2Foca.2241$$EPDF$$P50$$Gwiley$$H</linktopdf><linktohtml>$$Uhttps://onlinelibrary.wiley.com/doi/full/10.1002%2Foca.2241$$EHTML$$P50$$Gwiley$$H</linktohtml><link.rule.ids>314,776,780,1411,27901,27902,45550,45551</link.rule.ids></links><search><creatorcontrib>Kim, Kwang‐Ki K.</creatorcontrib><creatorcontrib>Braatz, Richard D.</creatorcontrib><title>Robust static and fixed‐order dynamic output feedback control of discrete‐time parametric uncertain Luré systems: Sequential SDP relaxation approaches</title><title>Optimal control applications & methods</title><description>Summary
Design methods are proposed for static and fixed‐order dynamic output feedback controllers for discrete‐time Luré systems with sector‐bounded nonlinearities in the presence of parametric uncertainties described by polytopes. The derived design conditions are represented in terms of bilinear matrix inequalities, which are nonconvex. By using convex relaxation methods, controller design equations are derived for systems with multiple states, outputs, and nonlinearities in terms of linear matrix inequalities (LMIs) and iterative LMIs, which are associated with semidefinite programs. The proposed design methods are developed from stability conditions using parameter‐dependent Lyapunov functions, and existing iterative numerical methods are adapted to solve certain classes of nonconvex optimization problems for controller design. Several numerical examples are provided to illustrate and verify the proposed design methods. Copyright © 2016 John Wiley & Sons, Ltd.</description><subject>Control methods</subject><subject>Controllers</subject><subject>Design engineering</subject><subject>Design parameters</subject><subject>Dynamical systems</subject><subject>fixed‐order dynamic output feedback control</subject><subject>Luré system</subject><subject>Mathematical analysis</subject><subject>Nonlinear dynamics</subject><subject>Nonlinearity</subject><subject>parameter‐dependent Lyapunov function</subject><subject>robust control</subject><subject>static output feedback control</subject><issn>0143-2087</issn><issn>1099-1514</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2017</creationdate><recordtype>article</recordtype><recordid>eNp1kUtqHDEQhoWxIWPHkCMIvMmmx3r1Q9kN4zwMAw5-rBu1VI3b7pbakprM7HKE7H2CnMM38UmiyRgMBq8Kqr6q-qt-hD5RMqeEsFOn1ZwxQffQjBIpM5pTsY9mhAqeMVKVH9BhCHeEkJJyNkOPl66ZQsQhqthprKzBbbcG8_z7j_MGPDYbq4ZUcVMcp4hbANMofY-1s9G7HrsWmy5oDxFST-wGwKPyaoDoU9dkNfioOotXk3_6i8MmRBjCF3wFDxPY2KkeX539xB56tU4KnMVqHL1T-hbCR3TQqj7A8Us8Qjffvl4vf2Sri-_ny8Uq05wVNIPCMFO2FRAjiGg4aSspGd-mctnkuSkrLhrCBdOCCVNwyWQuJCeKAjOm5Efo825uWpxUhVgP6SLoe2XBTaGmVZX-JdJXE3ryBr1zk7dJXaLyUhYFk_J1oPYuBA9tPfpuUH5TU1JvXaqTS_XWpYRmO_RX18PmXa6-WC7-8_8ArleXkg</recordid><startdate>201701</startdate><enddate>201701</enddate><creator>Kim, Kwang‐Ki K.</creator><creator>Braatz, Richard D.</creator><general>Wiley Subscription Services, Inc</general><scope>AAYXX</scope><scope>CITATION</scope><scope>7SP</scope><scope>8FD</scope><scope>JQ2</scope><scope>L7M</scope></search><sort><creationdate>201701</creationdate><title>Robust static and fixed‐order dynamic output feedback control of discrete‐time parametric uncertain Luré systems: Sequential SDP relaxation approaches</title><author>Kim, Kwang‐Ki K. ; Braatz, Richard D.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c3261-e6d2d7f8e0d404b30f89923d7f859b55d7834b0342c424d6392954930a1e2dd73</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2017</creationdate><topic>Control methods</topic><topic>Controllers</topic><topic>Design engineering</topic><topic>Design parameters</topic><topic>Dynamical systems</topic><topic>fixed‐order dynamic output feedback control</topic><topic>Luré system</topic><topic>Mathematical analysis</topic><topic>Nonlinear dynamics</topic><topic>Nonlinearity</topic><topic>parameter‐dependent Lyapunov function</topic><topic>robust control</topic><topic>static output feedback control</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Kim, Kwang‐Ki K.</creatorcontrib><creatorcontrib>Braatz, Richard D.</creatorcontrib><collection>CrossRef</collection><collection>Electronics & Communications Abstracts</collection><collection>Technology Research Database</collection><collection>ProQuest Computer Science Collection</collection><collection>Advanced Technologies Database with Aerospace</collection><jtitle>Optimal control applications & methods</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Kim, Kwang‐Ki K.</au><au>Braatz, Richard D.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Robust static and fixed‐order dynamic output feedback control of discrete‐time parametric uncertain Luré systems: Sequential SDP relaxation approaches</atitle><jtitle>Optimal control applications & methods</jtitle><date>2017-01</date><risdate>2017</risdate><volume>38</volume><issue>1</issue><spage>36</spage><epage>58</epage><pages>36-58</pages><issn>0143-2087</issn><eissn>1099-1514</eissn><coden>OCAMD5</coden><abstract>Summary
Design methods are proposed for static and fixed‐order dynamic output feedback controllers for discrete‐time Luré systems with sector‐bounded nonlinearities in the presence of parametric uncertainties described by polytopes. The derived design conditions are represented in terms of bilinear matrix inequalities, which are nonconvex. By using convex relaxation methods, controller design equations are derived for systems with multiple states, outputs, and nonlinearities in terms of linear matrix inequalities (LMIs) and iterative LMIs, which are associated with semidefinite programs. The proposed design methods are developed from stability conditions using parameter‐dependent Lyapunov functions, and existing iterative numerical methods are adapted to solve certain classes of nonconvex optimization problems for controller design. Several numerical examples are provided to illustrate and verify the proposed design methods. Copyright © 2016 John Wiley & Sons, Ltd.</abstract><cop>Glasgow</cop><pub>Wiley Subscription Services, Inc</pub><doi>10.1002/oca.2241</doi><tpages>23</tpages></addata></record> |
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| source | Wiley Online Library Journals Frontfile Complete |
| subjects | Control methods Controllers Design engineering Design parameters Dynamical systems fixed‐order dynamic output feedback control Luré system Mathematical analysis Nonlinear dynamics Nonlinearity parameter‐dependent Lyapunov function robust control static output feedback control |
| title | Robust static and fixed‐order dynamic output feedback control of discrete‐time parametric uncertain Luré systems: Sequential SDP relaxation approaches |
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