{"id":"https://openalex.org/W2009656020","doi":"https://doi.org/10.1109/tac.2013.2293451","title":"Stabilizing Linear Model Predictive Control Under Inexact Numerical Optimization","display_name":"Stabilizing Linear Model Predictive Control Under Inexact Numerical Optimization","publication_year":2014,"publication_date":"2014-01-31","ids":{"openalex":"https://openalex.org/W2009656020","doi":"https://doi.org/10.1109/tac.2013.2293451","mag":"2009656020"},"language":"en","primary_location":{"id":"doi:10.1109/tac.2013.2293451","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tac.2013.2293451","pdf_url":null,"source":{"id":"https://openalex.org/S184954342","display_name":"IEEE Transactions on Automatic Control","issn_l":"0018-9286","issn":["0018-9286","1558-2523","2334-3303"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Automatic Control","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://figshare.com/articles/journal_contribution/Stabilizing_Linear_Model_Predictive_Control_Under_Inexact_Numerical_Optimization/10168346","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5068220737","display_name":"Matteo Rubagotti","orcid":"https://orcid.org/0000-0002-3674-1455"},"institutions":[{"id":"https://openalex.org/I60559429","display_name":"Nazarbayev University","ror":"https://ror.org/052bx8q98","country_code":"KZ","type":"education","lineage":["https://openalex.org/I60559429"]}],"countries":["KZ"],"is_corresponding":true,"raw_author_name":"Matteo Rubagotti","raw_affiliation_strings":["Nazarbayev University (NU), Astana, Kazakhstan"],"affiliations":[{"raw_affiliation_string":"Nazarbayev University (NU), Astana, Kazakhstan","institution_ids":["https://openalex.org/I60559429"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5031380765","display_name":"Panagiotis Patrinos","orcid":"https://orcid.org/0000-0003-4824-7697"},"institutions":[{"id":"https://openalex.org/I127077003","display_name":"IMT School for Advanced Studies Lucca","ror":"https://ror.org/035gh3a49","country_code":"IT","type":"education","lineage":["https://openalex.org/I127077003"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Panagiotis Patrinos","raw_affiliation_strings":["IMT \u2013 Institute for Advanced Studies, Lucca, Italy","IMT \u2014 Institute for Advanced Studies Lucca, Italy"],"affiliations":[{"raw_affiliation_string":"IMT \u2013 Institute for Advanced Studies, Lucca, Italy","institution_ids":["https://openalex.org/I127077003"]},{"raw_affiliation_string":"IMT \u2014 Institute for Advanced Studies Lucca, Italy","institution_ids":["https://openalex.org/I127077003"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5053340099","display_name":"Alberto Bemporad","orcid":"https://orcid.org/0000-0001-6761-0856"},"institutions":[{"id":"https://openalex.org/I127077003","display_name":"IMT School for Advanced Studies Lucca","ror":"https://ror.org/035gh3a49","country_code":"IT","type":"education","lineage":["https://openalex.org/I127077003"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Alberto Bemporad","raw_affiliation_strings":["IMT \u2013 Institute for Advanced Studies, Lucca, Italy","IMT \u2014 Institute for Advanced Studies Lucca, Italy"],"affiliations":[{"raw_affiliation_string":"IMT \u2013 Institute for Advanced Studies, Lucca, Italy","institution_ids":["https://openalex.org/I127077003"]},{"raw_affiliation_string":"IMT \u2014 Institute for Advanced Studies Lucca, Italy","institution_ids":["https://openalex.org/I127077003"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5068220737"],"corresponding_institution_ids":["https://openalex.org/I60559429"],"apc_list":null,"apc_paid":null,"fwci":8.6143,"has_fulltext":false,"cited_by_count":56,"citation_normalized_percentile":{"value":0.97637209,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"59","issue":"6","first_page":"1660","last_page":"1666"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10791","display_name":"Advanced Control Systems Optimization","score":1.0,"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":1.0,"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/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9757000207901001,"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/T10046","display_name":"Stability and Control of Uncertain Systems","score":0.965499997138977,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/model-predictive-control","display_name":"Model predictive control","score":0.6909980773925781},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.604901134967804},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.5993489027023315},{"id":"https://openalex.org/keywords/optimal-control","display_name":"Optimal control","score":0.5344998240470886},{"id":"https://openalex.org/keywords/exponential-stability","display_name":"Exponential stability","score":0.5231838822364807},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5202575922012329},{"id":"https://openalex.org/keywords/optimization-problem","display_name":"Optimization problem","score":0.5044330358505249},{"id":"https://openalex.org/keywords/linear-system","display_name":"Linear system","score":0.47910597920417786},{"id":"https://openalex.org/keywords/quadratic-equation","display_name":"Quadratic equation","score":0.4654240310192108},{"id":"https://openalex.org/keywords/projection","display_name":"Projection (relational algebra)","score":0.45719093084335327},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.4305894672870636},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.4239666163921356},{"id":"https://openalex.org/keywords/quadratic-programming","display_name":"Quadratic programming","score":0.4219841957092285},{"id":"https://openalex.org/keywords/discrete-time-and-continuous-time","display_name":"Discrete time and continuous time","score":0.4168263077735901},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.35914838314056396},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.29842129349708557},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.1766417920589447},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.13739359378814697}],"concepts":[{"id":"https://openalex.org/C172205157","wikidata":"https://www.wikidata.org/wiki/Q1782962","display_name":"Model predictive control","level":3,"score":0.6909980773925781},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.604901134967804},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.5993489027023315},{"id":"https://openalex.org/C91575142","wikidata":"https://www.wikidata.org/wiki/Q1971426","display_name":"Optimal control","level":2,"score":0.5344998240470886},{"id":"https://openalex.org/C167964875","wikidata":"https://www.wikidata.org/wiki/Q17011487","display_name":"Exponential stability","level":3,"score":0.5231838822364807},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5202575922012329},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.5044330358505249},{"id":"https://openalex.org/C6802819","wikidata":"https://www.wikidata.org/wiki/Q1072174","display_name":"Linear system","level":2,"score":0.47910597920417786},{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.4654240310192108},{"id":"https://openalex.org/C57493831","wikidata":"https://www.wikidata.org/wiki/Q3134666","display_name":"Projection (relational algebra)","level":2,"score":0.45719093084335327},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.4305894672870636},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.4239666163921356},{"id":"https://openalex.org/C81845259","wikidata":"https://www.wikidata.org/wiki/Q290117","display_name":"Quadratic programming","level":2,"score":0.4219841957092285},{"id":"https://openalex.org/C55689738","wikidata":"https://www.wikidata.org/wiki/Q15963867","display_name":"Discrete time and continuous time","level":2,"score":0.4168263077735901},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.35914838314056396},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.29842129349708557},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.1766417920589447},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.13739359378814697},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","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},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1109/tac.2013.2293451","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tac.2013.2293451","pdf_url":null,"source":{"id":"https://openalex.org/S184954342","display_name":"IEEE Transactions on Automatic Control","issn_l":"0018-9286","issn":["0018-9286","1558-2523","2334-3303"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Automatic Control","raw_type":"journal-article"},{"id":"pmh:oai:figshare.com:article/10168346","is_oa":true,"landing_page_url":"https://figshare.com/articles/journal_contribution/Stabilizing_Linear_Model_Predictive_Control_Under_Inexact_Numerical_Optimization/10168346","pdf_url":null,"source":{"id":"https://openalex.org/S4377196282","display_name":"Figshare","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210132348","host_organization_name":"Figshare (United Kingdom)","host_organization_lineage":["https://openalex.org/I4210132348"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Text"},{"id":"pmh:oai:lirias2repo.kuleuven.be:123456789/533831","is_oa":false,"landing_page_url":"https://lirias.kuleuven.be/bitstream/123456789/533831/1/rubagotti2014stabilizing-1.pdf","pdf_url":null,"source":{"id":"https://openalex.org/S4306401954","display_name":"Lirias (KU Leuven)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I99464096","host_organization_name":"KU Leuven","host_organization_lineage":["https://openalex.org/I99464096"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"IEEE Transactions on Automatic Control, vol. 59 (6), Art.No. 6, (1660-1666)","raw_type":"info:eu-repo/semantics/publishedVersion"},{"id":"pmh:oai:lra.le.ac.uk:2381/37052","is_oa":false,"landing_page_url":"http://ieeexplore.ieee.org/xpl/articleDetails.jsp?arnumber=6725631","pdf_url":null,"source":{"id":"https://openalex.org/S4306402365","display_name":"Leicester Research Archive (University of Leicester)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I153648349","host_organization_name":"University of Leicester","host_organization_lineage":["https://openalex.org/I153648349"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Journal Article"}],"best_oa_location":{"id":"pmh:oai:figshare.com:article/10168346","is_oa":true,"landing_page_url":"https://figshare.com/articles/journal_contribution/Stabilizing_Linear_Model_Predictive_Control_Under_Inexact_Numerical_Optimization/10168346","pdf_url":null,"source":{"id":"https://openalex.org/S4377196282","display_name":"Figshare","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210132348","host_organization_name":"Figshare (United Kingdom)","host_organization_lineage":["https://openalex.org/I4210132348"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Text"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":29,"referenced_works":["https://openalex.org/W1583497301","https://openalex.org/W1627598360","https://openalex.org/W1859605168","https://openalex.org/W1920935944","https://openalex.org/W1964375219","https://openalex.org/W1980145158","https://openalex.org/W1981832695","https://openalex.org/W1983864916","https://openalex.org/W1985496293","https://openalex.org/W1989688414","https://openalex.org/W2026079951","https://openalex.org/W2034466934","https://openalex.org/W2073787051","https://openalex.org/W2090117039","https://openalex.org/W2106821132","https://openalex.org/W2109873351","https://openalex.org/W2111087336","https://openalex.org/W2116773335","https://openalex.org/W2124541940","https://openalex.org/W2127580532","https://openalex.org/W2138112069","https://openalex.org/W2165545652","https://openalex.org/W2171505650","https://openalex.org/W2936995161","https://openalex.org/W4206546401","https://openalex.org/W6638980285","https://openalex.org/W6640171395","https://openalex.org/W6647905349","https://openalex.org/W6680886281"],"related_works":["https://openalex.org/W2133946365","https://openalex.org/W1490558830","https://openalex.org/W568226970","https://openalex.org/W2898186729","https://openalex.org/W4242810725","https://openalex.org/W1993569878","https://openalex.org/W1580422375","https://openalex.org/W2370949144","https://openalex.org/W1591969690","https://openalex.org/W2072811658"],"abstract_inverted_index":{"This":[0,40],"note":[1],"describes":[2],"a":[3,69,85,125,152,160,167],"model":[4],"predictive":[5],"control":[6,17,45],"(MPC)":[7],"formulation":[8],"for":[9,47,129,139],"discrete-time":[10],"linear":[11],"systems":[12],"with":[13],"hard":[14],"constraints":[15,50],"on":[16,57,92,144,151],"and":[18,51,89,112],"state":[19],"variables,":[20],"under":[21],"the":[22,25,28,37,58,93,115,121,130,140,145],"assumption":[23],"that":[24,64,79,100,120,164],"solution":[26,123],"of":[27,61,95,110,114,171],"associated":[29],"quadratic":[30],"program":[31],"is":[32,41,75,90,124,137],"neither":[33],"optimal":[34],"nor":[35],"satisfies":[36],"inequality":[38,116],"constraints.":[39,117],"common":[42],"in":[43,78],"embedded":[44],"applications,":[46],"which":[48],"real-time":[49],"limited":[52],"computing":[53],"resources":[54],"dictate":[55],"restrictions":[56],"possible":[59],"number":[60,170],"on-line":[62,172],"iterations":[63],"can":[65,103],"be":[66,105],"performed":[67],"within":[68,107],"sampling":[70],"period.":[71],"The":[72],"proposed":[73],"approach":[74],"rather":[76],"general,":[77],"it":[80],"does":[81],"not":[82],"refer":[83],"to":[84,158],"particular":[86],"optimization":[87],"algorithm,":[88],"based":[91],"definition":[94],"an":[96],"alternative":[97],"MPC":[98,162],"problem":[99],"we":[101,149],"assume":[102],"only":[104,165],"solved":[106],"bounded":[108],"levels":[109],"suboptimality,":[111],"violation":[113],"By":[118],"showing":[119],"inexact":[122],"feasible":[126],"suboptimal":[127],"one":[128],"original":[131],"problem,":[132],"asymptotic":[133],"or":[134],"exponential":[135],"stability":[136],"guaranteed":[138],"closed-loop":[141],"system.":[142],"Based":[143],"above":[146],"general":[147],"results,":[148],"focus":[150],"specific":[153],"dual":[154],"accelerated":[155],"gradient-projection":[156],"method":[157],"obtain":[159],"stabilizing":[161],"law":[163],"requires":[166],"predetermined":[168],"maximum":[169],"iterations.":[173]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":7},{"year":2022,"cited_by_count":6},{"year":2021,"cited_by_count":6},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":4},{"year":2018,"cited_by_count":3},{"year":2017,"cited_by_count":6},{"year":2016,"cited_by_count":4},{"year":2015,"cited_by_count":9},{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":1}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}