{"id":"https://openalex.org/W3006078114","doi":"https://doi.org/10.1007/s10444-020-09744-8","title":"Feedback control of parametrized PDEs via model order reduction and dynamic programming principle","display_name":"Feedback control of parametrized PDEs via model order reduction and dynamic programming principle","publication_year":2020,"publication_date":"2020-01-01","ids":{"openalex":"https://openalex.org/W3006078114","doi":"https://doi.org/10.1007/s10444-020-09744-8","mag":"3006078114"},"language":"en","primary_location":{"id":"pmh:oai:iris.uniroma1.it:11573/1718154","is_oa":false,"landing_page_url":"https://hdl.handle.net/11573/1718154","pdf_url":null,"source":{"id":"https://openalex.org/S4377196107","display_name":"IRIS Research product catalog (Sapienza University of Rome)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"info:eu-repo/semantics/article"},"type":"article","indexed_in":[],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"http://hdl.handle.net/10278/3746313","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5102925000","display_name":"Alessandro Alla","orcid":"https://orcid.org/0000-0003-1832-1649"},"institutions":[{"id":"https://openalex.org/I2699952","display_name":"Pontif\u00edcia Universidade Cat\u00f3lica do Rio de Janeiro","ror":"https://ror.org/01dg47b60","country_code":"BR","type":"education","lineage":["https://openalex.org/I2699952"]}],"countries":["BR"],"is_corresponding":true,"raw_author_name":"Alla A.","raw_affiliation_strings":["Department of Mathematics, PUC-Rio, Rua Marques de S\u00e3o Vicente, 225, Rio de Janeiro, 22453-900, Brazil"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, PUC-Rio, Rua Marques de S\u00e3o Vicente, 225, Rio de Janeiro, 22453-900, Brazil","institution_ids":["https://openalex.org/I2699952"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5073837806","display_name":"Bernard Haasdonk","orcid":null},"institutions":[{"id":"https://openalex.org/I100066346","display_name":"University of Stuttgart","ror":"https://ror.org/04vnq7t77","country_code":"DE","type":"education","lineage":["https://openalex.org/I100066346"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Haasdonk B.","raw_affiliation_strings":["Institute of Applied Analysis and Numerical Simulation, University of Stuttgart, Pfaffenwaldring 57, 70569, Stuttgart, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute of Applied Analysis and Numerical Simulation, University of Stuttgart, Pfaffenwaldring 57, 70569, Stuttgart, Germany","institution_ids":["https://openalex.org/I100066346"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5101585981","display_name":"Andreas Schmidt","orcid":"https://orcid.org/0000-0002-9911-5881"},"institutions":[{"id":"https://openalex.org/I100066346","display_name":"University of Stuttgart","ror":"https://ror.org/04vnq7t77","country_code":"DE","type":"education","lineage":["https://openalex.org/I100066346"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Schmidt A.","raw_affiliation_strings":["Institute of Applied Analysis and Numerical Simulation, University of Stuttgart, Pfaffenwaldring 57, 70569, Stuttgart, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute of Applied Analysis and Numerical Simulation, University of Stuttgart, Pfaffenwaldring 57, 70569, Stuttgart, Germany","institution_ids":["https://openalex.org/I100066346"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5102925000"],"corresponding_institution_ids":["https://openalex.org/I2699952"],"apc_list":null,"apc_paid":null,"fwci":0.584,"has_fulltext":false,"cited_by_count":8,"citation_normalized_percentile":{"value":0.62016797,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11206","display_name":"Model Reduction and Neural Networks","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11206","display_name":"Model Reduction and Neural Networks","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11416","display_name":"Numerical methods for differential equations","score":0.9973999857902527,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10173","display_name":"Computational Fluid Dynamics and Aerodynamics","score":0.9914000034332275,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/dimensionality-reduction","display_name":"Dimensionality reduction","score":0.6580495834350586},{"id":"https://openalex.org/keywords/dynamic-programming","display_name":"Dynamic programming","score":0.6125203967094421},{"id":"https://openalex.org/keywords/curse-of-dimensionality","display_name":"Curse of dimensionality","score":0.5836045742034912},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.5791187286376953},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.547041118144989},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.543825626373291},{"id":"https://openalex.org/keywords/basis","display_name":"Basis (linear algebra)","score":0.5170524716377258},{"id":"https://openalex.org/keywords/optimal-control","display_name":"Optimal control","score":0.5092810392379761},{"id":"https://openalex.org/keywords/reduction","display_name":"Reduction (mathematics)","score":0.48824384808540344},{"id":"https://openalex.org/keywords/parametric-statistics","display_name":"Parametric statistics","score":0.4826529622077942},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.45931321382522583},{"id":"https://openalex.org/keywords/linear-subspace","display_name":"Linear subspace","score":0.45153293013572693},{"id":"https://openalex.org/keywords/model-order-reduction","display_name":"Model order reduction","score":0.4441068172454834},{"id":"https://openalex.org/keywords/domain","display_name":"Domain (mathematical analysis)","score":0.4366884231567383},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.43012258410453796},{"id":"https://openalex.org/keywords/differential-dynamic-programming","display_name":"Differential dynamic programming","score":0.42807719111442566},{"id":"https://openalex.org/keywords/basis-function","display_name":"Basis function","score":0.42061564326286316},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.2559710443019867},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.1088402271270752},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.10253366827964783}],"concepts":[{"id":"https://openalex.org/C70518039","wikidata":"https://www.wikidata.org/wiki/Q16000077","display_name":"Dimensionality reduction","level":2,"score":0.6580495834350586},{"id":"https://openalex.org/C37404715","wikidata":"https://www.wikidata.org/wiki/Q380679","display_name":"Dynamic programming","level":2,"score":0.6125203967094421},{"id":"https://openalex.org/C111030470","wikidata":"https://www.wikidata.org/wiki/Q1430460","display_name":"Curse of dimensionality","level":2,"score":0.5836045742034912},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.5791187286376953},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.547041118144989},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.543825626373291},{"id":"https://openalex.org/C12426560","wikidata":"https://www.wikidata.org/wiki/Q189569","display_name":"Basis (linear algebra)","level":2,"score":0.5170524716377258},{"id":"https://openalex.org/C91575142","wikidata":"https://www.wikidata.org/wiki/Q1971426","display_name":"Optimal control","level":2,"score":0.5092810392379761},{"id":"https://openalex.org/C111335779","wikidata":"https://www.wikidata.org/wiki/Q3454686","display_name":"Reduction (mathematics)","level":2,"score":0.48824384808540344},{"id":"https://openalex.org/C117251300","wikidata":"https://www.wikidata.org/wiki/Q1849855","display_name":"Parametric statistics","level":2,"score":0.4826529622077942},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.45931321382522583},{"id":"https://openalex.org/C12362212","wikidata":"https://www.wikidata.org/wiki/Q728435","display_name":"Linear subspace","level":2,"score":0.45153293013572693},{"id":"https://openalex.org/C2779277453","wikidata":"https://www.wikidata.org/wiki/Q12202921","display_name":"Model order reduction","level":3,"score":0.4441068172454834},{"id":"https://openalex.org/C36503486","wikidata":"https://www.wikidata.org/wiki/Q11235244","display_name":"Domain (mathematical analysis)","level":2,"score":0.4366884231567383},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.43012258410453796},{"id":"https://openalex.org/C92292787","wikidata":"https://www.wikidata.org/wiki/Q5275342","display_name":"Differential dynamic programming","level":3,"score":0.42807719111442566},{"id":"https://openalex.org/C5917680","wikidata":"https://www.wikidata.org/wiki/Q2621825","display_name":"Basis function","level":2,"score":0.42061564326286316},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.2559710443019867},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.1088402271270752},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.10253366827964783},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C57493831","wikidata":"https://www.wikidata.org/wiki/Q3134666","display_name":"Projection (relational algebra)","level":2,"score":0.0},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"pmh:oai:iris.uniroma1.it:11573/1718154","is_oa":false,"landing_page_url":"https://hdl.handle.net/11573/1718154","pdf_url":null,"source":{"id":"https://openalex.org/S4377196107","display_name":"IRIS Research product catalog (Sapienza University of Rome)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:iris.uniroma1.it:11573/1718168","is_oa":false,"landing_page_url":"https://hdl.handle.net/11573/1718168","pdf_url":null,"source":{"id":"https://openalex.org/S4377196107","display_name":"IRIS Research product catalog (Sapienza University of Rome)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:iris.unive.it:10278/3746313","is_oa":true,"landing_page_url":"http://hdl.handle.net/10278/3746313","pdf_url":null,"source":{"id":"https://openalex.org/S4306402336","display_name":"ARCA (Universit\u00e0 Ca' Foscari Venezia)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I149461666","host_organization_name":"Ca' Foscari University of Venice","host_organization_lineage":["https://openalex.org/I149461666"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":{"id":"pmh:oai:iris.unive.it:10278/3746313","is_oa":true,"landing_page_url":"http://hdl.handle.net/10278/3746313","pdf_url":null,"source":{"id":"https://openalex.org/S4306402336","display_name":"ARCA (Universit\u00e0 Ca' Foscari Venezia)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I149461666","host_organization_name":"Ca' Foscari University of Venice","host_organization_lineage":["https://openalex.org/I149461666"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"info:eu-repo/semantics/article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G2367254824","display_name":"DIAMOND: AN INTEGRATED MULTIFACETED APPROACH TO MATHEMATICS AT THE INTERFACES OF DATA, MODELS, AND DECISIONS","funder_award_id":"DESC0009324","funder_id":"https://openalex.org/F4320306084","funder_display_name":"U.S. Department of Energy"}],"funders":[{"id":"https://openalex.org/F4320306084","display_name":"U.S. Department of Energy","ror":"https://ror.org/01bj3aw27"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":42,"referenced_works":["https://openalex.org/W76493064","https://openalex.org/W176465980","https://openalex.org/W1487586009","https://openalex.org/W1551480811","https://openalex.org/W1600371943","https://openalex.org/W1631623342","https://openalex.org/W1991243721","https://openalex.org/W2012386000","https://openalex.org/W2014784776","https://openalex.org/W2019680819","https://openalex.org/W2021092589","https://openalex.org/W2026912249","https://openalex.org/W2028145673","https://openalex.org/W2047591100","https://openalex.org/W2049814048","https://openalex.org/W2055288447","https://openalex.org/W2061508005","https://openalex.org/W2077763222","https://openalex.org/W2085335060","https://openalex.org/W2088299544","https://openalex.org/W2122674116","https://openalex.org/W2124236693","https://openalex.org/W2132953997","https://openalex.org/W2148094730","https://openalex.org/W2149713433","https://openalex.org/W2152896489","https://openalex.org/W2228567937","https://openalex.org/W2249665386","https://openalex.org/W2269341318","https://openalex.org/W2324815854","https://openalex.org/W2341171179","https://openalex.org/W2463191373","https://openalex.org/W2488897645","https://openalex.org/W2587165485","https://openalex.org/W2588542536","https://openalex.org/W2802043810","https://openalex.org/W2924040522","https://openalex.org/W2963898648","https://openalex.org/W2964101103","https://openalex.org/W3101159108","https://openalex.org/W4210840654","https://openalex.org/W4302436361"],"related_works":["https://openalex.org/W4281717838","https://openalex.org/W4315488747","https://openalex.org/W2212478920","https://openalex.org/W2007971149","https://openalex.org/W761054003","https://openalex.org/W3012421647","https://openalex.org/W2052479296","https://openalex.org/W1996983632","https://openalex.org/W2061256745","https://openalex.org/W1986827546"],"abstract_inverted_index":{"In":[0],"this":[1],"paper,":[2],"we":[3,36,70,81,101],"investigate":[4],"infinite":[5],"horizon":[6],"optimal":[7],"control":[8,20,52],"problems":[9],"for":[10,113],"parametrized":[11],"partial":[12],"differential":[13],"equations.":[14],"We":[15],"are":[16],"interested":[17],"in":[18,90,115],"feedback":[19],"via":[21],"dynamic":[22,56],"programming":[23,57],"equations":[24,58],"which":[25,94],"is":[26,95],"well-known":[27],"to":[28,43,86,105],"suffer":[29],"from":[30],"the":[31,51,55,91,107,110],"curse":[32],"of":[33,67,109],"dimensionality.":[34],"Thus,":[35],"apply":[37],"parametric":[38],"model":[39],"order":[40],"reduction":[41],"techniques":[42],"construct":[44,87],"low-dimensional":[45],"subspaces":[46],"with":[47],"suitable":[48],"information":[49],"on":[50,97],"problem,":[53],"where":[54],"can":[59],"be":[60],"approximated.":[61],"To":[62],"guarantee":[63],"a":[64,83],"low":[65],"number":[66],"basis":[68,73],"functions,":[69],"combine":[71],"recent":[72],"generation":[74],"methods":[75,112],"and":[76],"parameter":[77],"partitioning":[78],"techniques.":[79],"Furthermore,":[80],"present":[82],"novel":[84],"technique":[85],"non-uniform":[88],"grids":[89],"reduced":[92],"domain,":[93],"based":[96],"statistical":[98],"information.":[99],"Finally,":[100],"discuss":[102],"numerical":[103],"examples":[104],"illustrate":[106],"effectiveness":[108],"proposed":[111],"PDEs":[114],"two":[116],"space":[117],"dimensions":[118]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":1}],"updated_date":"2026-08-08T01:25:22.217667","created_date":"2025-10-10T00:00:00"}