{"id":"https://openalex.org/W2805831706","doi":"https://doi.org/10.1109/lcsys.2018.2844730","title":"Solving Stochastic LQR Problems by Polynomial Chaos","display_name":"Solving Stochastic LQR Problems by Polynomial Chaos","publication_year":2018,"publication_date":"2018-06-07","ids":{"openalex":"https://openalex.org/W2805831706","doi":"https://doi.org/10.1109/lcsys.2018.2844730","mag":"2805831706"},"language":"en","primary_location":{"id":"doi:10.1109/lcsys.2018.2844730","is_oa":false,"landing_page_url":"https://doi.org/10.1109/lcsys.2018.2844730","pdf_url":null,"source":{"id":"https://openalex.org/S4306422535","display_name":"IEEE Control Systems Letters","issn_l":"2475-1456","issn":["2475-1456"],"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 Control Systems Letters","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/A5049009010","display_name":"Tijana Levajkovi\u0107","orcid":"https://orcid.org/0000-0002-1491-9056"},"institutions":[{"id":"https://openalex.org/I190249584","display_name":"Universit\u00e4t Innsbruck","ror":"https://ror.org/054pv6659","country_code":"AT","type":"education","lineage":["https://openalex.org/I190249584"]}],"countries":["AT"],"is_corresponding":true,"raw_author_name":"Tijana Levajkovic","raw_affiliation_strings":["Unit of Engineering Mathematics, University of Innsbruck, Innsbruck, Austria"],"raw_orcid":"https://orcid.org/0000-0002-1491-9056","affiliations":[{"raw_affiliation_string":"Unit of Engineering Mathematics, University of Innsbruck, Innsbruck, Austria","institution_ids":["https://openalex.org/I190249584"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5009359668","display_name":"Hermann Mena","orcid":null},"institutions":[{"id":"https://openalex.org/I190249584","display_name":"Universit\u00e4t Innsbruck","ror":"https://ror.org/054pv6659","country_code":"AT","type":"education","lineage":["https://openalex.org/I190249584"]}],"countries":["AT"],"is_corresponding":false,"raw_author_name":"Hermann Mena","raw_affiliation_strings":["Department of Mathematics, University of Innsbruck, Innsbruck, Austria"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Innsbruck, Innsbruck, Austria","institution_ids":["https://openalex.org/I190249584"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5034255902","display_name":"Lena-Maria Pfurtscheller","orcid":"https://orcid.org/0000-0002-2232-4159"},"institutions":[{"id":"https://openalex.org/I190249584","display_name":"Universit\u00e4t Innsbruck","ror":"https://ror.org/054pv6659","country_code":"AT","type":"education","lineage":["https://openalex.org/I190249584"]}],"countries":["AT"],"is_corresponding":false,"raw_author_name":"Lena-Maria Pfurtscheller","raw_affiliation_strings":["Department of Mathematics, University of Innsbruck, Innsbruck, Austria"],"raw_orcid":"https://orcid.org/0000-0002-2232-4159","affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Innsbruck, Innsbruck, Austria","institution_ids":["https://openalex.org/I190249584"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5049009010"],"corresponding_institution_ids":["https://openalex.org/I190249584"],"apc_list":null,"apc_paid":null,"fwci":0.399,"has_fulltext":false,"cited_by_count":4,"citation_normalized_percentile":{"value":0.6862186,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":96},"biblio":{"volume":"2","issue":"4","first_page":"641","last_page":"646"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10928","display_name":"Probabilistic and Robust Engineering Design","score":0.9993000030517578,"subfield":{"id":"https://openalex.org/subfields/1804","display_name":"Statistics, Probability and Uncertainty"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},"topics":[{"id":"https://openalex.org/T10928","display_name":"Probabilistic and Robust Engineering Design","score":0.9993000030517578,"subfield":{"id":"https://openalex.org/subfields/1804","display_name":"Statistics, Probability and Uncertainty"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T11513","display_name":"stochastic dynamics and bifurcation","score":0.9505000114440918,"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/T11236","display_name":"Control Systems and Identification","score":0.9343000054359436,"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/polynomial-chaos","display_name":"Polynomial chaos","score":0.8657732009887695},{"id":"https://openalex.org/keywords/linear-quadratic-regulator","display_name":"Linear-quadratic regulator","score":0.7748458981513977},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.699325442314148},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.6429803967475891},{"id":"https://openalex.org/keywords/optimal-control","display_name":"Optimal control","score":0.5801926851272583},{"id":"https://openalex.org/keywords/state-variable","display_name":"State variable","score":0.5666176676750183},{"id":"https://openalex.org/keywords/quadratic-equation","display_name":"Quadratic equation","score":0.47866615653038025},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.46859875321388245},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.4641519784927368},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.46357017755508423},{"id":"https://openalex.org/keywords/state","display_name":"State (computer science)","score":0.4206277132034302},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.4035106301307678},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.2355446219444275},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.17959028482437134},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.12422564625740051},{"id":"https://openalex.org/keywords/monte-carlo-method","display_name":"Monte Carlo method","score":0.09336981177330017}],"concepts":[{"id":"https://openalex.org/C197656079","wikidata":"https://www.wikidata.org/wiki/Q17147719","display_name":"Polynomial chaos","level":3,"score":0.8657732009887695},{"id":"https://openalex.org/C98779006","wikidata":"https://www.wikidata.org/wiki/Q2520550","display_name":"Linear-quadratic regulator","level":3,"score":0.7748458981513977},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.699325442314148},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.6429803967475891},{"id":"https://openalex.org/C91575142","wikidata":"https://www.wikidata.org/wiki/Q1971426","display_name":"Optimal control","level":2,"score":0.5801926851272583},{"id":"https://openalex.org/C129537906","wikidata":"https://www.wikidata.org/wiki/Q7603913","display_name":"State variable","level":2,"score":0.5666176676750183},{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.47866615653038025},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.46859875321388245},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.4641519784927368},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.46357017755508423},{"id":"https://openalex.org/C48103436","wikidata":"https://www.wikidata.org/wiki/Q599031","display_name":"State (computer science)","level":2,"score":0.4206277132034302},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.4035106301307678},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2355446219444275},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.17959028482437134},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.12422564625740051},{"id":"https://openalex.org/C19499675","wikidata":"https://www.wikidata.org/wiki/Q232207","display_name":"Monte Carlo method","level":2,"score":0.09336981177330017},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","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/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"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":1,"locations":[{"id":"doi:10.1109/lcsys.2018.2844730","is_oa":false,"landing_page_url":"https://doi.org/10.1109/lcsys.2018.2844730","pdf_url":null,"source":{"id":"https://openalex.org/S4306422535","display_name":"IEEE Control Systems Letters","issn_l":"2475-1456","issn":["2475-1456"],"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 Control Systems Letters","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G4651506474","display_name":null,"funder_award_id":"P27926","funder_id":"https://openalex.org/F4320321181","funder_display_name":"Austrian Science Fund"}],"funders":[{"id":"https://openalex.org/F4320321181","display_name":"Austrian Science Fund","ror":"https://ror.org/013tf3c58"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":27,"referenced_works":["https://openalex.org/W1527296550","https://openalex.org/W1584666263","https://openalex.org/W1969052444","https://openalex.org/W1978411015","https://openalex.org/W2018159038","https://openalex.org/W2036605062","https://openalex.org/W2054171246","https://openalex.org/W2056196028","https://openalex.org/W2066009815","https://openalex.org/W2066059560","https://openalex.org/W2069483977","https://openalex.org/W2074235022","https://openalex.org/W2095363071","https://openalex.org/W2110936503","https://openalex.org/W2134065371","https://openalex.org/W2331552525","https://openalex.org/W2344818275","https://openalex.org/W2592816500","https://openalex.org/W2595442784","https://openalex.org/W2750492110","https://openalex.org/W2963758004","https://openalex.org/W3103608114","https://openalex.org/W4243373887","https://openalex.org/W4292027189","https://openalex.org/W4300475775","https://openalex.org/W6734405795","https://openalex.org/W6749648567"],"related_works":["https://openalex.org/W339217817","https://openalex.org/W2797263970","https://openalex.org/W2891782306","https://openalex.org/W2287391662","https://openalex.org/W4381886630","https://openalex.org/W2203843426","https://openalex.org/W2805831706","https://openalex.org/W2049369111","https://openalex.org/W2113133070","https://openalex.org/W1974638344"],"abstract_inverted_index":{"We":[0,16,63,85,106],"consider":[1],"the":[2,12,33,39,54,57,60,87,90,96,103,116],"infinite":[3,13,78,119],"dimensional":[4],"stochastic":[5],"linear":[6,81],"quadratic":[7,82],"optimal":[8],"control":[9,61,67],"problem":[10,24,68],"for":[11,21,69],"horizon":[14,79,120],"case.":[15,121],"provide":[17],"a":[18,26,44,66,75],"numerical":[19,108],"framework":[20],"solving":[22],"this":[23],"using":[25],"polynomial":[27],"chaos":[28,36],"expansion":[29,97],"approach.":[30,105],"By":[31],"applying":[32],"method":[34],"of":[35,46,53,56,77,89,95,98],"expansions":[37],"to":[38,102],"state":[40,58],"equation,":[41,71],"we":[42],"obtain":[43],"system":[45],"deterministic":[47,80],"partial":[48],"differential":[49],"equations":[50],"in":[51,74,93],"terms":[52,94],"coefficients":[55,100],"and":[59,114,118],"variables.":[62],"set":[64,76],"up":[65],"each":[70],"which":[72,110],"results":[73],"regulator":[83],"problems.":[84],"prove":[86],"optimality":[88],"solution":[91],"expressed":[92],"these":[99],"compared":[101],"direct":[104],"perform":[107],"experiments":[109],"validate":[111],"our":[112],"approach":[113],"compare":[115],"finite":[117]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2020,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}