{"id":"https://openalex.org/W3214796166","doi":"https://doi.org/10.1007/s00498-022-00325-2","title":"The turnpike property and the longtime behavior of the Hamilton\u2013Jacobi\u2013Bellman equation for finite-dimensional LQ control problems","display_name":"The turnpike property and the longtime behavior of the Hamilton\u2013Jacobi\u2013Bellman equation for finite-dimensional LQ control problems","publication_year":2022,"publication_date":"2022-06-16","ids":{"openalex":"https://openalex.org/W3214796166","doi":"https://doi.org/10.1007/s00498-022-00325-2","mag":"3214796166"},"language":"en","primary_location":{"id":"doi:10.1007/s00498-022-00325-2","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s00498-022-00325-2","pdf_url":null,"source":{"id":"https://openalex.org/S88345224","display_name":"Mathematics of Control Signals and Systems","issn_l":"0932-4194","issn":["0932-4194","1435-568X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Control, Signals, and Systems","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2006.10430","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5066476801","display_name":"Carlos Esteve","orcid":"https://orcid.org/0000-0002-8671-0163"},"institutions":[{"id":"https://openalex.org/I136040515","display_name":"Universidad de Deusto","ror":"https://ror.org/00ne6sr39","country_code":"ES","type":"education","lineage":["https://openalex.org/I136040515"]},{"id":"https://openalex.org/I63634437","display_name":"Universidad Aut\u00f3noma de Madrid","ror":"https://ror.org/01cby8j38","country_code":"ES","type":"education","lineage":["https://openalex.org/I63634437"]}],"countries":["ES"],"is_corresponding":true,"raw_author_name":"Carlos Esteve","raw_affiliation_strings":["Chair of Computational Mathematics, Fundaci\u00f3n Deusto, Av. de las Universidades, 24, 48007, Bilbao, Basque Country, Spain","Departamento de Matem\u00e1ticas, Universidad Aut\u00f3noma de Madrid, 28049, Madrid, Spain"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Chair of Computational Mathematics, Fundaci\u00f3n Deusto, Av. de las Universidades, 24, 48007, Bilbao, Basque Country, Spain","institution_ids":["https://openalex.org/I136040515"]},{"raw_affiliation_string":"Departamento de Matem\u00e1ticas, Universidad Aut\u00f3noma de Madrid, 28049, Madrid, Spain","institution_ids":["https://openalex.org/I63634437"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5036280716","display_name":"Hicham Kouhkouh","orcid":"https://orcid.org/0000-0002-2632-448X"},"institutions":[{"id":"https://openalex.org/I138689650","display_name":"University of Padua","ror":"https://ror.org/00240q980","country_code":"IT","type":"education","lineage":["https://openalex.org/I138689650"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Hicham Kouhkouh","raw_affiliation_strings":["Dipartimento di Matematica, Universit\u00e0 di Padova, Via Trieste, 63, 35121, Padua, Italy"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Dipartimento di Matematica, Universit\u00e0 di Padova, Via Trieste, 63, 35121, Padua, Italy","institution_ids":["https://openalex.org/I138689650"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5001020344","display_name":"Dar\u00edo Pighin","orcid":"https://orcid.org/0000-0001-5181-7350"},"institutions":[{"id":"https://openalex.org/I136040515","display_name":"Universidad de Deusto","ror":"https://ror.org/00ne6sr39","country_code":"ES","type":"education","lineage":["https://openalex.org/I136040515"]},{"id":"https://openalex.org/I63634437","display_name":"Universidad Aut\u00f3noma de Madrid","ror":"https://ror.org/01cby8j38","country_code":"ES","type":"education","lineage":["https://openalex.org/I63634437"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"Dario Pighin","raw_affiliation_strings":["Chair of Computational Mathematics, Fundaci\u00f3n Deusto, Av. de las Universidades, 24, 48007, Bilbao, Basque Country, Spain","Departamento de Matem\u00e1ticas, Universidad Aut\u00f3noma de Madrid, 28049, Madrid, Spain"],"raw_orcid":"https://orcid.org/0000-0001-5181-7350","affiliations":[{"raw_affiliation_string":"Chair of Computational Mathematics, Fundaci\u00f3n Deusto, Av. de las Universidades, 24, 48007, Bilbao, Basque Country, Spain","institution_ids":["https://openalex.org/I136040515"]},{"raw_affiliation_string":"Departamento de Matem\u00e1ticas, Universidad Aut\u00f3noma de Madrid, 28049, Madrid, Spain","institution_ids":["https://openalex.org/I63634437"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5088702266","display_name":"Enrique Zuazua","orcid":"https://orcid.org/0000-0002-1377-0958"},"institutions":[{"id":"https://openalex.org/I136040515","display_name":"Universidad de Deusto","ror":"https://ror.org/00ne6sr39","country_code":"ES","type":"education","lineage":["https://openalex.org/I136040515"]},{"id":"https://openalex.org/I181369854","display_name":"Friedrich-Alexander-Universit\u00e4t Erlangen-N\u00fcrnberg","ror":"https://ror.org/00f7hpc57","country_code":"DE","type":"education","lineage":["https://openalex.org/I181369854"]},{"id":"https://openalex.org/I63634437","display_name":"Universidad Aut\u00f3noma de Madrid","ror":"https://ror.org/01cby8j38","country_code":"ES","type":"education","lineage":["https://openalex.org/I63634437"]}],"countries":["DE","ES"],"is_corresponding":false,"raw_author_name":"Enrique Zuazua","raw_affiliation_strings":["Chair of Computational Mathematics, Fundaci\u00f3n Deusto, Av. de las Universidades, 24, 48007, Bilbao, Basque Country, Spain","Departamento de Matem\u00e1ticas, Universidad Aut\u00f3noma de Madrid, 28049, Madrid, Spain","Department of Data Science, Friedrich-Alexander-Universit\u00e4t Erlangen-N\u00fcrnberg, 91058, Erlangen, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Chair of Computational Mathematics, Fundaci\u00f3n Deusto, Av. de las Universidades, 24, 48007, Bilbao, Basque Country, Spain","institution_ids":["https://openalex.org/I136040515"]},{"raw_affiliation_string":"Departamento de Matem\u00e1ticas, Universidad Aut\u00f3noma de Madrid, 28049, Madrid, Spain","institution_ids":["https://openalex.org/I63634437"]},{"raw_affiliation_string":"Department of Data Science, Friedrich-Alexander-Universit\u00e4t Erlangen-N\u00fcrnberg, 91058, Erlangen, Germany","institution_ids":["https://openalex.org/I181369854"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5066476801"],"corresponding_institution_ids":["https://openalex.org/I136040515","https://openalex.org/I63634437"],"apc_list":{"value":2390,"currency":"EUR","value_usd":2990},"apc_paid":null,"fwci":1.0476,"has_fulltext":false,"cited_by_count":6,"citation_normalized_percentile":{"value":0.76413137,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"34","issue":"4","first_page":"819","last_page":"853"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10067","display_name":"Stochastic processes and financial applications","score":0.9955999851226807,"subfield":{"id":"https://openalex.org/subfields/2003","display_name":"Finance"},"field":{"id":"https://openalex.org/fields/20","display_name":"Economics, Econometrics and Finance"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},"topics":[{"id":"https://openalex.org/T10067","display_name":"Stochastic processes and financial applications","score":0.9955999851226807,"subfield":{"id":"https://openalex.org/subfields/2003","display_name":"Finance"},"field":{"id":"https://openalex.org/fields/20","display_name":"Economics, Econometrics and Finance"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T10940","display_name":"Navier-Stokes equation solutions","score":0.9757999777793884,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"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/T11110","display_name":"Stability and Controllability of Differential Equations","score":0.9681000113487244,"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/bellman-equation","display_name":"Bellman equation","score":0.7743308544158936},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6845198273658752},{"id":"https://openalex.org/keywords/optimal-control","display_name":"Optimal control","score":0.6734718680381775},{"id":"https://openalex.org/keywords/hamiltonian","display_name":"Hamiltonian (control theory)","score":0.613749623298645},{"id":"https://openalex.org/keywords/hamilton\u2013jacobi-equation","display_name":"Hamilton\u2013Jacobi equation","score":0.573141872882843},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4594351649284363},{"id":"https://openalex.org/keywords/property","display_name":"Property (philosophy)","score":0.43891578912734985},{"id":"https://openalex.org/keywords/quadratic-equation","display_name":"Quadratic equation","score":0.4185377061367035},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3303547501564026}],"concepts":[{"id":"https://openalex.org/C14646407","wikidata":"https://www.wikidata.org/wiki/Q1430750","display_name":"Bellman equation","level":2,"score":0.7743308544158936},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6845198273658752},{"id":"https://openalex.org/C91575142","wikidata":"https://www.wikidata.org/wiki/Q1971426","display_name":"Optimal control","level":2,"score":0.6734718680381775},{"id":"https://openalex.org/C130787639","wikidata":"https://www.wikidata.org/wiki/Q5645293","display_name":"Hamiltonian (control theory)","level":2,"score":0.613749623298645},{"id":"https://openalex.org/C2778860007","wikidata":"https://www.wikidata.org/wiki/Q1060137","display_name":"Hamilton\u2013Jacobi equation","level":2,"score":0.573141872882843},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4594351649284363},{"id":"https://openalex.org/C189950617","wikidata":"https://www.wikidata.org/wiki/Q937228","display_name":"Property (philosophy)","level":2,"score":0.43891578912734985},{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.4185377061367035},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3303547501564026},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"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/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1007/s00498-022-00325-2","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s00498-022-00325-2","pdf_url":null,"source":{"id":"https://openalex.org/S88345224","display_name":"Mathematics of Control Signals and Systems","issn_l":"0932-4194","issn":["0932-4194","1435-568X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Control, Signals, and Systems","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:2006.10430","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2006.10430","pdf_url":"https://arxiv.org/pdf/2006.10430","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":"pmh:oai:HAL:hal-03861524v1","is_oa":false,"landing_page_url":"https://hal.science/hal-03861524","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Mathematics of Control, Signals, and Systems, 2022, ⟨10.1007/s00498-022-00325-2⟩","raw_type":"Journal articles"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2006.10430","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2006.10430","pdf_url":"https://arxiv.org/pdf/2006.10430","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":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":51,"referenced_works":["https://openalex.org/W21944519","https://openalex.org/W1209334740","https://openalex.org/W1487586009","https://openalex.org/W1494380031","https://openalex.org/W1494982173","https://openalex.org/W1522531528","https://openalex.org/W1532111732","https://openalex.org/W1551784909","https://openalex.org/W1631623342","https://openalex.org/W1965640670","https://openalex.org/W1968010891","https://openalex.org/W1971804534","https://openalex.org/W1996270146","https://openalex.org/W2002357820","https://openalex.org/W2003588897","https://openalex.org/W2018219999","https://openalex.org/W2028808207","https://openalex.org/W2032316144","https://openalex.org/W2044948548","https://openalex.org/W2051631857","https://openalex.org/W2053068479","https://openalex.org/W2060088282","https://openalex.org/W2060542320","https://openalex.org/W2079261393","https://openalex.org/W2079895693","https://openalex.org/W2102040002","https://openalex.org/W2112507254","https://openalex.org/W2138405426","https://openalex.org/W2247494051","https://openalex.org/W2282793296","https://openalex.org/W2465241486","https://openalex.org/W2529725405","https://openalex.org/W2556018921","https://openalex.org/W2604640182","https://openalex.org/W2612727995","https://openalex.org/W2613633283","https://openalex.org/W2749408143","https://openalex.org/W2755331706","https://openalex.org/W2793725483","https://openalex.org/W2796471654","https://openalex.org/W2962753423","https://openalex.org/W2991649084","https://openalex.org/W3006545585","https://openalex.org/W3015724939","https://openalex.org/W3021722416","https://openalex.org/W3045592875","https://openalex.org/W3104707106","https://openalex.org/W3106834257","https://openalex.org/W3150803659","https://openalex.org/W3205687719","https://openalex.org/W4292078458"],"related_works":["https://openalex.org/W1985696076","https://openalex.org/W1977330547","https://openalex.org/W1974495512","https://openalex.org/W4226406511","https://openalex.org/W4390746698","https://openalex.org/W4286890456","https://openalex.org/W2061850819","https://openalex.org/W1996243804","https://openalex.org/W1983345526","https://openalex.org/W2503339255"],"abstract_inverted_index":null,"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}