{"id":"https://openalex.org/W4213123361","doi":"https://doi.org/10.1137/20m1356324","title":"Efficient Model Predictive Control for Parabolic PDEs with Goal Oriented Error Estimation","display_name":"Efficient Model Predictive Control for Parabolic PDEs with Goal Oriented Error Estimation","publication_year":2022,"publication_date":"2022-02-01","ids":{"openalex":"https://openalex.org/W4213123361","doi":"https://doi.org/10.1137/20m1356324"},"language":"en","primary_location":{"id":"doi:10.1137/20m1356324","is_oa":false,"landing_page_url":"https://doi.org/10.1137/20m1356324","pdf_url":null,"source":{"id":"https://openalex.org/S165512578","display_name":"SIAM Journal on Scientific Computing","issn_l":"1064-8275","issn":["1064-8275","1095-7197"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Scientific Computing","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5054568856","display_name":"Lars Gr\u00fcne","orcid":"https://orcid.org/0000-0002-9331-4097"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Lars Gr\u00fcne","raw_affiliation_strings":[],"raw_orcid":"https://orcid.org/0000-0002-9331-4097","affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5002858094","display_name":"Manuel Schaller","orcid":"https://orcid.org/0000-0002-8081-5108"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Manuel Schaller","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5040824080","display_name":"Anton Schiela","orcid":"https://orcid.org/0000-0002-6959-2951"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Anton Schiela","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.2136,"has_fulltext":false,"cited_by_count":13,"citation_normalized_percentile":{"value":0.77209953,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"44","issue":"1","first_page":"A471","last_page":"A500"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10791","display_name":"Advanced Control Systems Optimization","score":0.9998000264167786,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10791","display_name":"Advanced Control Systems Optimization","score":0.9998000264167786,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11110","display_name":"Stability and Controllability of Differential Equations","score":0.9839000105857849,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.9749000072479248,"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/model-predictive-control","display_name":"Model predictive control","score":0.7330873608589172},{"id":"https://openalex.org/keywords/context","display_name":"Context (archaeology)","score":0.6696513891220093},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6172605156898499},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.6136773228645325},{"id":"https://openalex.org/keywords/a-priori-and-a-posteriori","display_name":"A priori and a posteriori","score":0.6078600287437439},{"id":"https://openalex.org/keywords/grid","display_name":"Grid","score":0.531766951084137},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4805736541748047},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.4330919682979584},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3942264914512634},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.3700944483280182},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.06774502992630005}],"concepts":[{"id":"https://openalex.org/C172205157","wikidata":"https://www.wikidata.org/wiki/Q1782962","display_name":"Model predictive control","level":3,"score":0.7330873608589172},{"id":"https://openalex.org/C2779343474","wikidata":"https://www.wikidata.org/wiki/Q3109175","display_name":"Context (archaeology)","level":2,"score":0.6696513891220093},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6172605156898499},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.6136773228645325},{"id":"https://openalex.org/C75553542","wikidata":"https://www.wikidata.org/wiki/Q178161","display_name":"A priori and a posteriori","level":2,"score":0.6078600287437439},{"id":"https://openalex.org/C187691185","wikidata":"https://www.wikidata.org/wiki/Q2020720","display_name":"Grid","level":2,"score":0.531766951084137},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4805736541748047},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.4330919682979584},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3942264914512634},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.3700944483280182},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.06774502992630005},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C151730666","wikidata":"https://www.wikidata.org/wiki/Q7205","display_name":"Paleontology","level":1,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/20m1356324","is_oa":false,"landing_page_url":"https://doi.org/10.1137/20m1356324","pdf_url":null,"source":{"id":"https://openalex.org/S165512578","display_name":"SIAM Journal on Scientific Computing","issn_l":"1064-8275","issn":["1064-8275","1095-7197"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Scientific Computing","raw_type":"journal-article"},{"id":"pmh:oai:eref.uni-bayreuth.de:68749","is_oa":false,"landing_page_url":"https://eref.uni-bayreuth.de/68749/","pdf_url":null,"source":{"id":"https://openalex.org/S4377196442","display_name":"ERef Bayreuth (University of Bayreuth)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I54009628","host_organization_name":"University of Bayreuth","host_organization_lineage":["https://openalex.org/I54009628"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Artikel in einer Zeitschrift"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G308758612","display_name":null,"funder_award_id":"1569/17-1","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"},{"id":"https://openalex.org/G4642623073","display_name":null,"funder_award_id":"1379/5-1","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"}],"funders":[{"id":"https://openalex.org/F4320320879","display_name":"Deutsche Forschungsgemeinschaft","ror":"https://ror.org/018mejw64"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":24,"referenced_works":["https://openalex.org/W1976803805","https://openalex.org/W1981159109","https://openalex.org/W1989951672","https://openalex.org/W1998967184","https://openalex.org/W2008621392","https://openalex.org/W2008736432","https://openalex.org/W2039924562","https://openalex.org/W2060088282","https://openalex.org/W2060546108","https://openalex.org/W2082118157","https://openalex.org/W2090807663","https://openalex.org/W2100267011","https://openalex.org/W2133147107","https://openalex.org/W2134673975","https://openalex.org/W2170507823","https://openalex.org/W2282793296","https://openalex.org/W2582992792","https://openalex.org/W2808390209","https://openalex.org/W2887155241","https://openalex.org/W2898464076","https://openalex.org/W2904139432","https://openalex.org/W2945041002","https://openalex.org/W3010181856","https://openalex.org/W3137907199"],"related_works":["https://openalex.org/W1990079087","https://openalex.org/W2060165215","https://openalex.org/W4388311650","https://openalex.org/W2101188133","https://openalex.org/W1974056099","https://openalex.org/W3202234113","https://openalex.org/W4245343541","https://openalex.org/W2386077341","https://openalex.org/W563589758","https://openalex.org/W2556120871"],"abstract_inverted_index":{"We":[0],"show":[1],"how":[2],"a":[3,19,32,38,54],"posteriori":[4],"goal":[5,62],"oriented":[6,63],"error":[7,71],"estimation":[8],"can":[9],"be":[10],"used":[11],"to":[12,46,83],"efficiently":[13],"solve":[14],"the":[15,76],"subproblems":[16],"occurring":[17],"in":[18],"model":[20],"predictive":[21],"control":[22],"(MPC)":[23],"algorithm.":[24],"In":[25],"MPC,":[26,91],"only":[27],"an":[28,59],"initial":[29],"part":[30],"of":[31,78,98],"computed":[33],"solution":[34],"is":[35],"implemented":[36],"as":[37,58],"feedback,":[39],"which":[40,92],"motivates":[41],"grid":[42],"refinement":[43],"particularly":[44],"tailored":[45],"this":[47,50,79],"context.":[48],"To":[49],"end,":[51],"we":[52,93],"present":[53],"truncated":[55],"cost":[56],"functional":[57],"objective":[60],"for":[61,90],"adaptivity":[64],"and":[65,87],"prove":[66],"under":[67],"stabilizability":[68],"assumptions":[69],"that":[70],"indicators":[72],"decay":[73],"exponentially":[74],"outside":[75],"support":[77],"quantity.":[80],"This":[81],"leads":[82],"very":[84],"efficient":[85],"time":[86],"space":[88],"discretizations":[89],"will":[94],"illustrate":[95],"by":[96],"means":[97],"various":[99],"numerical":[100],"examples.":[101]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":4},{"year":2020,"cited_by_count":1}],"updated_date":"2026-06-17T08:01:34.144755","created_date":"2025-10-10T00:00:00"}
