{"id":"https://openalex.org/W2117419845","doi":"https://doi.org/10.1109/cdc.2005.1583267","title":"Power Series Solution of the Hamilton-Jacobi-Bellman Equation for Descriptor Systems","display_name":"Power Series Solution of the Hamilton-Jacobi-Bellman Equation for Descriptor Systems","publication_year":2006,"publication_date":"2006-10-04","ids":{"openalex":"https://openalex.org/W2117419845","doi":"https://doi.org/10.1109/cdc.2005.1583267","mag":"2117419845"},"language":"en","primary_location":{"id":"doi:10.1109/cdc.2005.1583267","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cdc.2005.1583267","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 44th IEEE Conference on Decision and Control","raw_type":"proceedings-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-56039","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5064731323","display_name":"Johan Sj\u00f6berg","orcid":"https://orcid.org/0000-0003-4563-3808"},"institutions":[{"id":"https://openalex.org/I102134673","display_name":"Link\u00f6ping University","ror":"https://ror.org/05ynxx418","country_code":"SE","type":"education","lineage":["https://openalex.org/I102134673"]}],"countries":["SE"],"is_corresponding":true,"raw_author_name":"J. Sjoberg","raw_affiliation_strings":["Department of Electrical Engineering, Link\u00f6ping Universitet, Linkoping, Sweden","Division of Automatic Control, Department of Electrical Engineering, Link\u00f6pings universitet, SE-581 83 Link\u00f6ping, SWEDEN. johans@isy.liu.se"],"affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering, Link\u00f6ping Universitet, Linkoping, Sweden","institution_ids":["https://openalex.org/I102134673"]},{"raw_affiliation_string":"Division of Automatic Control, Department of Electrical Engineering, Link\u00f6pings universitet, SE-581 83 Link\u00f6ping, SWEDEN. johans@isy.liu.se","institution_ids":["https://openalex.org/I102134673"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5050599460","display_name":"Torkel Glad","orcid":null},"institutions":[{"id":"https://openalex.org/I102134673","display_name":"Link\u00f6ping University","ror":"https://ror.org/05ynxx418","country_code":"SE","type":"education","lineage":["https://openalex.org/I102134673"]}],"countries":["SE"],"is_corresponding":false,"raw_author_name":"T. Glad","raw_affiliation_strings":["Department of Electrical Engineering, Link\u00f6ping Universitet, Linkoping, Sweden","Link\u00f6ping University,#TAB#"],"affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering, Link\u00f6ping Universitet, Linkoping, Sweden","institution_ids":["https://openalex.org/I102134673"]},{"raw_affiliation_string":"Link\u00f6ping University,#TAB#","institution_ids":["https://openalex.org/I102134673"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5064731323"],"corresponding_institution_ids":["https://openalex.org/I102134673"],"apc_list":null,"apc_paid":null,"fwci":5.5023,"has_fulltext":false,"cited_by_count":6,"citation_normalized_percentile":{"value":0.95322334,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":null,"biblio":{"volume":"11","issue":null,"first_page":"6869","last_page":"6874"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11110","display_name":"Stability and Controllability of Differential Equations","score":0.9968000054359436,"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/T11110","display_name":"Stability and Controllability of Differential Equations","score":0.9968000054359436,"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/T13855","display_name":"Aerospace Engineering and Control Systems","score":0.9966999888420105,"subfield":{"id":"https://openalex.org/subfields/2202","display_name":"Aerospace 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/T10046","display_name":"Stability and Control of Uncertain Systems","score":0.9965999722480774,"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/hamilton\u2013jacobi-equation","display_name":"Hamilton\u2013Jacobi equation","score":0.7258733510971069},{"id":"https://openalex.org/keywords/series","display_name":"Series (stratigraphy)","score":0.7019315958023071},{"id":"https://openalex.org/keywords/power-series","display_name":"Power series","score":0.6526118516921997},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.6378868222236633},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.5792860388755798},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5588725209236145},{"id":"https://openalex.org/keywords/bellman-equation","display_name":"Bellman equation","score":0.5468490123748779},{"id":"https://openalex.org/keywords/optimal-control","display_name":"Optimal control","score":0.5421174764633179},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.5145508646965027},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5073747038841248},{"id":"https://openalex.org/keywords/hamilton\u2013jacobi\u2013bellman-equation","display_name":"Hamilton\u2013Jacobi\u2013Bellman equation","score":0.450467050075531},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.4224560260772705},{"id":"https://openalex.org/keywords/power","display_name":"Power (physics)","score":0.4180620014667511},{"id":"https://openalex.org/keywords/formal-power-series","display_name":"Formal power series","score":0.4149986505508423},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3766424059867859},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.3511563539505005},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3278296887874603},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.24940210580825806},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.07191017270088196},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.06936362385749817}],"concepts":[{"id":"https://openalex.org/C2778860007","wikidata":"https://www.wikidata.org/wiki/Q1060137","display_name":"Hamilton\u2013Jacobi equation","level":2,"score":0.7258733510971069},{"id":"https://openalex.org/C143724316","wikidata":"https://www.wikidata.org/wiki/Q312468","display_name":"Series (stratigraphy)","level":2,"score":0.7019315958023071},{"id":"https://openalex.org/C73905626","wikidata":"https://www.wikidata.org/wiki/Q206925","display_name":"Power series","level":2,"score":0.6526118516921997},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.6378868222236633},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.5792860388755798},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5588725209236145},{"id":"https://openalex.org/C14646407","wikidata":"https://www.wikidata.org/wiki/Q1430750","display_name":"Bellman equation","level":2,"score":0.5468490123748779},{"id":"https://openalex.org/C91575142","wikidata":"https://www.wikidata.org/wiki/Q1971426","display_name":"Optimal control","level":2,"score":0.5421174764633179},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.5145508646965027},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5073747038841248},{"id":"https://openalex.org/C196978813","wikidata":"https://www.wikidata.org/wiki/Q3302775","display_name":"Hamilton\u2013Jacobi\u2013Bellman equation","level":3,"score":0.450467050075531},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.4224560260772705},{"id":"https://openalex.org/C163258240","wikidata":"https://www.wikidata.org/wiki/Q25342","display_name":"Power (physics)","level":2,"score":0.4180620014667511},{"id":"https://openalex.org/C151746172","wikidata":"https://www.wikidata.org/wiki/Q1003025","display_name":"Formal power series","level":3,"score":0.4149986505508423},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3766424059867859},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.3511563539505005},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3278296887874603},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.24940210580825806},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.07191017270088196},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.06936362385749817},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"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/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","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}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/cdc.2005.1583267","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cdc.2005.1583267","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 44th IEEE Conference on Decision and Control","raw_type":"proceedings-article"},{"id":"pmh:oai:DiVA.org:liu-56039","is_oa":true,"landing_page_url":"http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-56039","pdf_url":null,"source":{"id":"https://openalex.org/S4306401559","display_name":"KTH Publication Database DiVA (KTH Royal Institute of Technology)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Report"}],"best_oa_location":{"id":"pmh:oai:DiVA.org:liu-56039","is_oa":true,"landing_page_url":"http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-56039","pdf_url":null,"source":{"id":"https://openalex.org/S4306401559","display_name":"KTH Publication Database DiVA (KTH Royal Institute of Technology)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Report"},"sustainable_development_goals":[{"score":0.8100000023841858,"id":"https://metadata.un.org/sdg/16","display_name":"Peace, Justice and strong institutions"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":17,"referenced_works":["https://openalex.org/W12260108","https://openalex.org/W151868298","https://openalex.org/W1492186721","https://openalex.org/W1516758666","https://openalex.org/W1593679773","https://openalex.org/W1966397236","https://openalex.org/W2072433108","https://openalex.org/W2075151302","https://openalex.org/W2077730310","https://openalex.org/W2102040002","https://openalex.org/W2112257557","https://openalex.org/W2128518031","https://openalex.org/W2159294788","https://openalex.org/W2162747898","https://openalex.org/W2321052409","https://openalex.org/W2796471654","https://openalex.org/W4301649152"],"related_works":["https://openalex.org/W2032834442","https://openalex.org/W3153900688","https://openalex.org/W2115544975","https://openalex.org/W2902017027","https://openalex.org/W1654696814","https://openalex.org/W4291598237","https://openalex.org/W2766998270","https://openalex.org/W4292330635","https://openalex.org/W3168988147","https://openalex.org/W1996904445"],"abstract_inverted_index":{"Optimal":[0],"control":[1,49],"problems":[2],"for":[3,40],"a":[4,18,24],"class":[5],"of":[6,26,44],"nonlinear":[7],"descriptor":[8],"systems":[9],"are":[10,36,51],"considered.":[11],"It":[12],"is":[13],"shown":[14],"that":[15],"they":[16],"possess":[17],"well-defined":[19],"analytical":[20],"feedback":[21],"solution":[22],"in":[23],"neighborhood":[25],"the":[27,41,45],"origin,":[28],"provided":[29],"stabilizability":[30],"and":[31,48],"some":[32],"other":[33],"regularity":[34],"conditions":[35],"satisfied.":[37],"Explicit":[38],"formulas":[39],"series":[42],"expansions":[43],"cost":[46],"function":[47],"law":[50],"given.":[52]},"counts_by_year":[],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}