On the use of reduced models obtained through identification for feedback optimal control problems in a heat convection–diffusion problem
This paper deals with the use of reduced models for solving some optimal control problems. More precisely, the reduced model is obtained through the modal identification method. The test case which the algorithms is tested on is based on the flow over a backward-facing step. Though the reduction for...
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| Veröffentlicht in: | Computer methods in applied mechanics and engineering 2010-03, Vol.199 (17), p.1193-1201 |
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| creator | Favennec, Y. Rouizi, Y. Petit, D. |
| description | This paper deals with the use of reduced models for solving some optimal control problems. More precisely, the reduced model is obtained through the modal identification method. The test case which the algorithms is tested on is based on the flow over a backward-facing step. Though the reduction for the velocity fields for different Reynolds numbers is treated elsewhere
[1], only the convection–diffusion equation for the energy problem is treated here. The model reduction is obtained through the solution of a gradient-type optimization problem where the objective function gradient is computed through the adjoint-state method. The obtained reduced models are validated before being coupled to optimal control algorithms. In this paper the feedback optimal control problem is considered. A Riccati equation is solved along with the Kalman gain equation. Additionally, a Kalman filter is performed to reconstruct the reduced state through previous and actual measurements. The numerical test case shows the ability of the proposed approach to control systems through the use of reduced models obtained by the modal identification method. |
| doi_str_mv | 10.1016/j.cma.2009.12.009 |
| format | Article |
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[1], only the convection–diffusion equation for the energy problem is treated here. The model reduction is obtained through the solution of a gradient-type optimization problem where the objective function gradient is computed through the adjoint-state method. The obtained reduced models are validated before being coupled to optimal control algorithms. In this paper the feedback optimal control problem is considered. A Riccati equation is solved along with the Kalman gain equation. Additionally, a Kalman filter is performed to reconstruct the reduced state through previous and actual measurements. The numerical test case shows the ability of the proposed approach to control systems through the use of reduced models obtained by the modal identification method.</description><identifier>ISSN: 0045-7825</identifier><identifier>EISSN: 1879-2138</identifier><identifier>DOI: 10.1016/j.cma.2009.12.009</identifier><identifier>CODEN: CMMECC</identifier><language>eng</language><publisher>Kidlington: Elsevier B.V</publisher><subject>Adjoint state method ; Algorithms ; Analytical and numerical techniques ; Backward-facing step ; Control systems ; Control theory ; Convection and heat transfer ; Exact sciences and technology ; Feedback ; Feedback control ; Fluid dynamics ; Fundamental areas of phenomenology (including applications) ; General theory ; Heat transfer ; Kalman filter ; Kalman gain ; Mathematical analysis ; Mathematical models ; Mathematical Physics ; Mathematics ; Measurement and testing methods ; Modal identification ; Modal identification method ; Model reduction ; Optimal control ; Optimization ; Physics ; Riccati equation ; Solid mechanics ; State estimation ; Structural and continuum mechanics ; Turbulent flows, convection, and heat transfer</subject><ispartof>Computer methods in applied mechanics and engineering, 2010-03, Vol.199 (17), p.1193-1201</ispartof><rights>2009 Elsevier B.V.</rights><rights>2015 INIST-CNRS</rights><rights>Distributed under a Creative Commons Attribution 4.0 International License</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c394t-8b862941f5adeea5669e4a65d84512dc041a9eb6b50616b822e4c59b8db17ac93</citedby><cites>FETCH-LOGICAL-c394t-8b862941f5adeea5669e4a65d84512dc041a9eb6b50616b822e4c59b8db17ac93</cites><orcidid>0000-0001-8806-3353 ; 0000-0001-8809-0706</orcidid></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktohtml>$$Uhttps://www.sciencedirect.com/science/article/pii/S0045782509004150$$EHTML$$P50$$Gelsevier$$H</linktohtml><link.rule.ids>230,314,776,780,881,3537,27901,27902,65306</link.rule.ids><backlink>$$Uhttp://pascal-francis.inist.fr/vibad/index.php?action=getRecordDetail&idt=22586224$$DView record in Pascal Francis$$Hfree_for_read</backlink><backlink>$$Uhttps://hal.science/hal-02324400$$DView record in HAL$$Hfree_for_read</backlink></links><search><creatorcontrib>Favennec, Y.</creatorcontrib><creatorcontrib>Rouizi, Y.</creatorcontrib><creatorcontrib>Petit, D.</creatorcontrib><title>On the use of reduced models obtained through identification for feedback optimal control problems in a heat convection–diffusion problem</title><title>Computer methods in applied mechanics and engineering</title><description>This paper deals with the use of reduced models for solving some optimal control problems. More precisely, the reduced model is obtained through the modal identification method. The test case which the algorithms is tested on is based on the flow over a backward-facing step. Though the reduction for the velocity fields for different Reynolds numbers is treated elsewhere
[1], only the convection–diffusion equation for the energy problem is treated here. The model reduction is obtained through the solution of a gradient-type optimization problem where the objective function gradient is computed through the adjoint-state method. The obtained reduced models are validated before being coupled to optimal control algorithms. In this paper the feedback optimal control problem is considered. A Riccati equation is solved along with the Kalman gain equation. Additionally, a Kalman filter is performed to reconstruct the reduced state through previous and actual measurements. The numerical test case shows the ability of the proposed approach to control systems through the use of reduced models obtained by the modal identification method.</description><subject>Adjoint state method</subject><subject>Algorithms</subject><subject>Analytical and numerical techniques</subject><subject>Backward-facing step</subject><subject>Control systems</subject><subject>Control theory</subject><subject>Convection and heat transfer</subject><subject>Exact sciences and technology</subject><subject>Feedback</subject><subject>Feedback control</subject><subject>Fluid dynamics</subject><subject>Fundamental areas of phenomenology (including applications)</subject><subject>General theory</subject><subject>Heat transfer</subject><subject>Kalman filter</subject><subject>Kalman gain</subject><subject>Mathematical analysis</subject><subject>Mathematical models</subject><subject>Mathematical Physics</subject><subject>Mathematics</subject><subject>Measurement and testing methods</subject><subject>Modal identification</subject><subject>Modal identification method</subject><subject>Model reduction</subject><subject>Optimal control</subject><subject>Optimization</subject><subject>Physics</subject><subject>Riccati equation</subject><subject>Solid mechanics</subject><subject>State estimation</subject><subject>Structural and continuum mechanics</subject><subject>Turbulent flows, convection, and heat transfer</subject><issn>0045-7825</issn><issn>1879-2138</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2010</creationdate><recordtype>article</recordtype><recordid>eNp9kcFu3CAQhq2qkbpN8gC9canUHuwCi22snqIoTSqtlEtzRmMYara22QJeKbfee-wb9kmKtascy-UX8M0_A39RvGO0YpQ1n_aVnqDilHYV41WWV8WGybYrOdvK18WGUlGXreT1m-JtjHual2R8U_x-nEkakCwRibckoFk0GjJ5g2Mkvk_g5rxPQ_DL94E4g3Ny1mlIzs_E-kAsoulB_yD-kNwEI9F-TsGP5BB8P-IUiZsJkAEhrVdH1Gvp319_jLN2iavNmbwqLiyMEa_Pelk8fbn7dvtQ7h7vv97e7Eq97UQqZS8b3glmazCIUDdNhwKa2khRM240FQw67Ju-pg1resk5Cl13vTQ9a0F328vi48l3gFEdQh46PCsPTj3c7NR6RvmWC0HpkWX2w4nNM_5cMCY1uahxHGFGv0TFmpZx3nIpMspOqA4-xoD2xZtRtYak9iqHpNaQFOMqS655f7aHqGG0AWbt4ksh53V-K1-9P5-4nAoeHQYVtcM5R-VC_lBlvPtPl39bWKmn</recordid><startdate>20100301</startdate><enddate>20100301</enddate><creator>Favennec, Y.</creator><creator>Rouizi, Y.</creator><creator>Petit, D.</creator><general>Elsevier B.V</general><general>Elsevier</general><scope>IQODW</scope><scope>AAYXX</scope><scope>CITATION</scope><scope>7SC</scope><scope>7TB</scope><scope>8FD</scope><scope>FR3</scope><scope>H8D</scope><scope>JQ2</scope><scope>KR7</scope><scope>L7M</scope><scope>L~C</scope><scope>L~D</scope><scope>1XC</scope><orcidid>https://orcid.org/0000-0001-8806-3353</orcidid><orcidid>https://orcid.org/0000-0001-8809-0706</orcidid></search><sort><creationdate>20100301</creationdate><title>On the use of reduced models obtained through identification for feedback optimal control problems in a heat convection–diffusion problem</title><author>Favennec, Y. ; Rouizi, Y. ; Petit, D.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c394t-8b862941f5adeea5669e4a65d84512dc041a9eb6b50616b822e4c59b8db17ac93</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2010</creationdate><topic>Adjoint state method</topic><topic>Algorithms</topic><topic>Analytical and numerical techniques</topic><topic>Backward-facing step</topic><topic>Control systems</topic><topic>Control theory</topic><topic>Convection and heat transfer</topic><topic>Exact sciences and technology</topic><topic>Feedback</topic><topic>Feedback control</topic><topic>Fluid dynamics</topic><topic>Fundamental areas of phenomenology (including applications)</topic><topic>General theory</topic><topic>Heat transfer</topic><topic>Kalman filter</topic><topic>Kalman gain</topic><topic>Mathematical analysis</topic><topic>Mathematical models</topic><topic>Mathematical Physics</topic><topic>Mathematics</topic><topic>Measurement and testing methods</topic><topic>Modal identification</topic><topic>Modal identification method</topic><topic>Model reduction</topic><topic>Optimal control</topic><topic>Optimization</topic><topic>Physics</topic><topic>Riccati equation</topic><topic>Solid mechanics</topic><topic>State estimation</topic><topic>Structural and continuum mechanics</topic><topic>Turbulent flows, convection, and heat transfer</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Favennec, Y.</creatorcontrib><creatorcontrib>Rouizi, Y.</creatorcontrib><creatorcontrib>Petit, D.</creatorcontrib><collection>Pascal-Francis</collection><collection>CrossRef</collection><collection>Computer and Information Systems Abstracts</collection><collection>Mechanical & Transportation Engineering Abstracts</collection><collection>Technology Research Database</collection><collection>Engineering Research Database</collection><collection>Aerospace Database</collection><collection>ProQuest Computer Science Collection</collection><collection>Civil Engineering Abstracts</collection><collection>Advanced Technologies Database with Aerospace</collection><collection>Computer and Information Systems Abstracts Academic</collection><collection>Computer and Information Systems Abstracts Professional</collection><collection>Hyper Article en Ligne (HAL)</collection><jtitle>Computer methods in applied mechanics and engineering</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Favennec, Y.</au><au>Rouizi, Y.</au><au>Petit, D.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>On the use of reduced models obtained through identification for feedback optimal control problems in a heat convection–diffusion problem</atitle><jtitle>Computer methods in applied mechanics and engineering</jtitle><date>2010-03-01</date><risdate>2010</risdate><volume>199</volume><issue>17</issue><spage>1193</spage><epage>1201</epage><pages>1193-1201</pages><issn>0045-7825</issn><eissn>1879-2138</eissn><coden>CMMECC</coden><abstract>This paper deals with the use of reduced models for solving some optimal control problems. 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[1], only the convection–diffusion equation for the energy problem is treated here. The model reduction is obtained through the solution of a gradient-type optimization problem where the objective function gradient is computed through the adjoint-state method. The obtained reduced models are validated before being coupled to optimal control algorithms. In this paper the feedback optimal control problem is considered. A Riccati equation is solved along with the Kalman gain equation. Additionally, a Kalman filter is performed to reconstruct the reduced state through previous and actual measurements. The numerical test case shows the ability of the proposed approach to control systems through the use of reduced models obtained by the modal identification method.</abstract><cop>Kidlington</cop><pub>Elsevier B.V</pub><doi>10.1016/j.cma.2009.12.009</doi><tpages>9</tpages><orcidid>https://orcid.org/0000-0001-8806-3353</orcidid><orcidid>https://orcid.org/0000-0001-8809-0706</orcidid></addata></record> |
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| ispartof | Computer methods in applied mechanics and engineering, 2010-03, Vol.199 (17), p.1193-1201 |
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| language | eng |
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| source | Elsevier ScienceDirect Journals |
| subjects | Adjoint state method Algorithms Analytical and numerical techniques Backward-facing step Control systems Control theory Convection and heat transfer Exact sciences and technology Feedback Feedback control Fluid dynamics Fundamental areas of phenomenology (including applications) General theory Heat transfer Kalman filter Kalman gain Mathematical analysis Mathematical models Mathematical Physics Mathematics Measurement and testing methods Modal identification Modal identification method Model reduction Optimal control Optimization Physics Riccati equation Solid mechanics State estimation Structural and continuum mechanics Turbulent flows, convection, and heat transfer |
| title | On the use of reduced models obtained through identification for feedback optimal control problems in a heat convection–diffusion problem |
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