{"id":"https://openalex.org/W2000714860","doi":"https://doi.org/10.1137/070685051","title":"Nonlinear Optimal Control via Occupation Measures and LMI-Relaxations","display_name":"Nonlinear Optimal Control via Occupation Measures and LMI-Relaxations","publication_year":2008,"publication_date":"2008-01-01","ids":{"openalex":"https://openalex.org/W2000714860","doi":"https://doi.org/10.1137/070685051","mag":"2000714860"},"language":"en","primary_location":{"id":"doi:10.1137/070685051","is_oa":false,"landing_page_url":"https://doi.org/10.1137/070685051","pdf_url":null,"source":{"id":"https://openalex.org/S897311980","display_name":"SIAM Journal on Control and Optimization","issn_l":"0363-0129","issn":["0363-0129","1095-7138"],"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 Control and Optimization","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/math/0703377","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5006670993","display_name":"Jean B. Lasserre","orcid":"https://orcid.org/0000-0003-0860-9913"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Jean B. Lasserre","raw_affiliation_strings":["lasserre@laas.fr#TAB#"],"affiliations":[{"raw_affiliation_string":"lasserre@laas.fr#TAB#","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5074893139","display_name":"Didier Henrion","orcid":"https://orcid.org/0000-0001-6735-7715"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Didier Henrion","raw_affiliation_strings":["[email\u00a0protected]#TAB#"],"affiliations":[{"raw_affiliation_string":"[email\u00a0protected]#TAB#","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5083387069","display_name":"Christophe Prieur","orcid":"https://orcid.org/0000-0002-4456-2019"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Christophe Prieur","raw_affiliation_strings":["cprieur@laas.fr#TAB#"],"affiliations":[{"raw_affiliation_string":"cprieur@laas.fr#TAB#","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5089339704","display_name":"Emmanuel Tr\u00e9lat","orcid":"https://orcid.org/0000-0002-0656-7003"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Emmanuel Tr\u00e9lat","raw_affiliation_strings":["emmanuel.trelat@univ-orleans.fr#TAB#"],"affiliations":[{"raw_affiliation_string":"emmanuel.trelat@univ-orleans.fr#TAB#","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5006670993"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":9.2789,"has_fulltext":false,"cited_by_count":276,"citation_normalized_percentile":{"value":0.98116633,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":99,"max":100},"biblio":{"volume":"47","issue":"4","first_page":"1643","last_page":"1666"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9987999796867371,"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"}},"topics":[{"id":"https://openalex.org/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9987999796867371,"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":0.9944000244140625,"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/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9897000193595886,"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/mathematics","display_name":"Mathematics","score":0.894002377986908},{"id":"https://openalex.org/keywords/sequence","display_name":"Sequence (biology)","score":0.7019615173339844},{"id":"https://openalex.org/keywords/optimal-control","display_name":"Optimal control","score":0.6603167653083801},{"id":"https://openalex.org/keywords/convexity","display_name":"Convexity","score":0.6336371898651123},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.567380964756012},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4932803511619568},{"id":"https://openalex.org/keywords/state","display_name":"State (computer science)","score":0.48777252435684204},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.4724317491054535},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.4674338400363922},{"id":"https://openalex.org/keywords/linear-matrix-inequality","display_name":"Linear matrix inequality","score":0.45962417125701904},{"id":"https://openalex.org/keywords/hierarchy","display_name":"Hierarchy","score":0.42246484756469727},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3858380615711212},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.3640638589859009},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.3318042457103729},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.2018926739692688},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.07017076015472412},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.06913036108016968}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.894002377986908},{"id":"https://openalex.org/C2778112365","wikidata":"https://www.wikidata.org/wiki/Q3511065","display_name":"Sequence (biology)","level":2,"score":0.7019615173339844},{"id":"https://openalex.org/C91575142","wikidata":"https://www.wikidata.org/wiki/Q1971426","display_name":"Optimal control","level":2,"score":0.6603167653083801},{"id":"https://openalex.org/C72134830","wikidata":"https://www.wikidata.org/wiki/Q5166524","display_name":"Convexity","level":2,"score":0.6336371898651123},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.567380964756012},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4932803511619568},{"id":"https://openalex.org/C48103436","wikidata":"https://www.wikidata.org/wiki/Q599031","display_name":"State (computer science)","level":2,"score":0.48777252435684204},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.4724317491054535},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.4674338400363922},{"id":"https://openalex.org/C201829737","wikidata":"https://www.wikidata.org/wiki/Q2022760","display_name":"Linear matrix inequality","level":2,"score":0.45962417125701904},{"id":"https://openalex.org/C31170391","wikidata":"https://www.wikidata.org/wiki/Q188619","display_name":"Hierarchy","level":2,"score":0.42246484756469727},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3858380615711212},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.3640638589859009},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.3318042457103729},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2018926739692688},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.07017076015472412},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.06913036108016968},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"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/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0},{"id":"https://openalex.org/C34447519","wikidata":"https://www.wikidata.org/wiki/Q179522","display_name":"Market economy","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C54355233","wikidata":"https://www.wikidata.org/wiki/Q7162","display_name":"Genetics","level":1,"score":0.0},{"id":"https://openalex.org/C106159729","wikidata":"https://www.wikidata.org/wiki/Q2294553","display_name":"Financial economics","level":1,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1137/070685051","is_oa":false,"landing_page_url":"https://doi.org/10.1137/070685051","pdf_url":null,"source":{"id":"https://openalex.org/S897311980","display_name":"SIAM Journal on Control and Optimization","issn_l":"0363-0129","issn":["0363-0129","1095-7138"],"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 Control and Optimization","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:math/0703377","is_oa":true,"landing_page_url":"http://arxiv.org/abs/math/0703377","pdf_url":"https://arxiv.org/pdf/math/0703377","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"text"},{"id":"doi:10.48550/arxiv.math/0703377","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.math/0703377","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:math/0703377","is_oa":true,"landing_page_url":"http://arxiv.org/abs/math/0703377","pdf_url":"https://arxiv.org/pdf/math/0703377","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"text"},"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/10","score":0.4300000071525574,"display_name":"Reduced inequalities"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":53,"referenced_works":["https://openalex.org/W99708544","https://openalex.org/W113966369","https://openalex.org/W118602349","https://openalex.org/W261814290","https://openalex.org/W1481789702","https://openalex.org/W1507296508","https://openalex.org/W1535396202","https://openalex.org/W1554655067","https://openalex.org/W1587799944","https://openalex.org/W1966305649","https://openalex.org/W1967344706","https://openalex.org/W1971044547","https://openalex.org/W1971947347","https://openalex.org/W1976237319","https://openalex.org/W1982019931","https://openalex.org/W1990337648","https://openalex.org/W2001981441","https://openalex.org/W2010654234","https://openalex.org/W2020032007","https://openalex.org/W2042963469","https://openalex.org/W2044060118","https://openalex.org/W2053199928","https://openalex.org/W2056823730","https://openalex.org/W2068098627","https://openalex.org/W2076020921","https://openalex.org/W2077658674","https://openalex.org/W2082219004","https://openalex.org/W2083746174","https://openalex.org/W2087002964","https://openalex.org/W2101003581","https://openalex.org/W2105260964","https://openalex.org/W2109339972","https://openalex.org/W2125283177","https://openalex.org/W2134489088","https://openalex.org/W2141616022","https://openalex.org/W2183870517","https://openalex.org/W2323201333","https://openalex.org/W2502655619","https://openalex.org/W2596682183","https://openalex.org/W2599068435","https://openalex.org/W3173138228","https://openalex.org/W4205353090","https://openalex.org/W4210545817","https://openalex.org/W4235840289","https://openalex.org/W4236316114","https://openalex.org/W4238377091","https://openalex.org/W4242771523","https://openalex.org/W4253201987","https://openalex.org/W4254742099","https://openalex.org/W4255442211","https://openalex.org/W4256525584","https://openalex.org/W4285538211","https://openalex.org/W4301866048"],"related_works":["https://openalex.org/W1964872188","https://openalex.org/W2187391117","https://openalex.org/W1981809986","https://openalex.org/W2949367465","https://openalex.org/W2587048717","https://openalex.org/W4235203617","https://openalex.org/W2006359264","https://openalex.org/W3029201158","https://openalex.org/W4794847","https://openalex.org/W2056357792"],"abstract_inverted_index":{"We":[0,50],"consider":[1],"the":[2,14,72,80,84,88],"class":[3],"of":[4,55,68,87],"nonlinear":[5],"optimal":[6,62,73,85],"control":[7,19],"problems":[8],"(OCP)":[9],"with":[10,34,98],"polynomial":[11],"data,":[12],"i.e.,":[13],"differential":[15],"equation,":[16],"state":[17,39,44],"and":[18,22,29],"con-":[20],"straints":[21],"cost":[23],"are":[24,48,96],"all":[25],"described":[26],"by":[27],"polynomials,":[28],"more":[30],"generally":[31],"for":[32],"OCPs":[33],"smooth":[35],"data.":[36],"In":[37],"addition,":[38],"constraints":[40,47],"as":[41,43],"well":[42],"and/or":[45],"action":[46],"allowed.":[49],"provide":[51],"a":[52,65],"simple":[53],"hierarchy":[54],"LMI":[56],"(lin-":[57],"ear":[58],"matrix":[59],"inequality)-relaxations":[60],"whose":[61],"values":[63],"form":[64],"nondecreasing":[66],"sequence":[67,81],"lower":[69],"bounds":[70],"on":[71],"value.":[74],"Under":[75],"some":[76],"convexity":[77],"assump-":[78],"tions,":[79],"converges":[82],"to":[83],"value":[86],"OCP.":[89],"Preliminary":[90],"results":[91],"show":[92],"that":[93],"good":[94],"approximations":[95],"obtained":[97],"few":[99],"moments.":[100]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":16},{"year":2024,"cited_by_count":19},{"year":2023,"cited_by_count":15},{"year":2022,"cited_by_count":19},{"year":2021,"cited_by_count":20},{"year":2020,"cited_by_count":19},{"year":2019,"cited_by_count":26},{"year":2018,"cited_by_count":26},{"year":2017,"cited_by_count":16},{"year":2016,"cited_by_count":11},{"year":2015,"cited_by_count":13},{"year":2014,"cited_by_count":27},{"year":2013,"cited_by_count":18},{"year":2012,"cited_by_count":11}],"updated_date":"2026-03-20T23:20:44.827607","created_date":"2022-08-13T00:00:00"}
