{"id":"https://openalex.org/W1983536992","doi":"https://doi.org/10.1137/s0363012998340223","title":"Degenerate Optimal Control Problems with State Constraints","display_name":"Degenerate Optimal Control Problems with State Constraints","publication_year":2000,"publication_date":"2000-01-01","ids":{"openalex":"https://openalex.org/W1983536992","doi":"https://doi.org/10.1137/s0363012998340223","mag":"1983536992"},"language":"en","primary_location":{"id":"doi:10.1137/s0363012998340223","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0363012998340223","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":["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/A5033202825","display_name":"Franco Rampazzo","orcid":"https://orcid.org/0000-0002-4195-7621"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Franco Rampazzo","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5031053402","display_name":"Richard Vinter","orcid":"https://orcid.org/0000-0002-3585-0473"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Richard Vinter","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5033202825"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":3.1793,"has_fulltext":false,"cited_by_count":67,"citation_normalized_percentile":{"value":0.91313823,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"39","issue":"4","first_page":"989","last_page":"1007"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10545","display_name":"Optimization and Variational Analysis","score":0.9988999962806702,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10545","display_name":"Optimization and Variational Analysis","score":0.9988999962806702,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10791","display_name":"Advanced Control Systems Optimization","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/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9914000034332275,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8494328260421753},{"id":"https://openalex.org/keywords/state","display_name":"State (computer science)","score":0.7046488523483276},{"id":"https://openalex.org/keywords/constraint","display_name":"Constraint (computer-aided design)","score":0.6246204972267151},{"id":"https://openalex.org/keywords/optimal-control","display_name":"Optimal control","score":0.5745143890380859},{"id":"https://openalex.org/keywords/trajectory","display_name":"Trajectory","score":0.5175678133964539},{"id":"https://openalex.org/keywords/boundary","display_name":"Boundary (topology)","score":0.5028173327445984},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.5023465156555176},{"id":"https://openalex.org/keywords/degenerate-energy-levels","display_name":"Degenerate energy levels","score":0.4953233301639557},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.4722180664539337},{"id":"https://openalex.org/keywords/dynamic-programming","display_name":"Dynamic programming","score":0.4590955376625061},{"id":"https://openalex.org/keywords/lagrange-multiplier","display_name":"Lagrange multiplier","score":0.4549110233783722},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.34537172317504883},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.17452001571655273},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.17145073413848877},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.11221036314964294},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.07253292202949524}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8494328260421753},{"id":"https://openalex.org/C48103436","wikidata":"https://www.wikidata.org/wiki/Q599031","display_name":"State (computer science)","level":2,"score":0.7046488523483276},{"id":"https://openalex.org/C2776036281","wikidata":"https://www.wikidata.org/wiki/Q48769818","display_name":"Constraint (computer-aided design)","level":2,"score":0.6246204972267151},{"id":"https://openalex.org/C91575142","wikidata":"https://www.wikidata.org/wiki/Q1971426","display_name":"Optimal control","level":2,"score":0.5745143890380859},{"id":"https://openalex.org/C13662910","wikidata":"https://www.wikidata.org/wiki/Q193139","display_name":"Trajectory","level":2,"score":0.5175678133964539},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.5028173327445984},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.5023465156555176},{"id":"https://openalex.org/C72319582","wikidata":"https://www.wikidata.org/wiki/Q584304","display_name":"Degenerate energy levels","level":2,"score":0.4953233301639557},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.4722180664539337},{"id":"https://openalex.org/C37404715","wikidata":"https://www.wikidata.org/wiki/Q380679","display_name":"Dynamic programming","level":2,"score":0.4590955376625061},{"id":"https://openalex.org/C73684929","wikidata":"https://www.wikidata.org/wiki/Q598870","display_name":"Lagrange multiplier","level":2,"score":0.4549110233783722},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.34537172317504883},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.17452001571655273},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.17145073413848877},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.11221036314964294},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.07253292202949524},{"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/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/C1276947","wikidata":"https://www.wikidata.org/wiki/Q333","display_name":"Astronomy","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/s0363012998340223","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0363012998340223","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:www.research.unipd.it:11577/1365468","is_oa":false,"landing_page_url":"http://apps.webofknowledge.com/full_record.do?product=UA&search_mode=GeneralSearch&qid=9&SID=Y2cKeBAGJCjhL37MOAb&page=1&doc=1","pdf_url":null,"source":{"id":"https://openalex.org/S4377196283","display_name":"Research Padua  Archive (University of Padua)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I138689650","host_organization_name":"University of Padua","host_organization_lineage":["https://openalex.org/I138689650"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":18,"referenced_works":["https://openalex.org/W1481022403","https://openalex.org/W1487326569","https://openalex.org/W1568090445","https://openalex.org/W1976930521","https://openalex.org/W2001405973","https://openalex.org/W2001720647","https://openalex.org/W2028582150","https://openalex.org/W2040647563","https://openalex.org/W2043888047","https://openalex.org/W2044710367","https://openalex.org/W2059777252","https://openalex.org/W2059999341","https://openalex.org/W2069746992","https://openalex.org/W2088117943","https://openalex.org/W2093020024","https://openalex.org/W2132325680","https://openalex.org/W2141616022","https://openalex.org/W4240902880"],"related_works":["https://openalex.org/W3206234362","https://openalex.org/W1932159282","https://openalex.org/W4285537323","https://openalex.org/W2379312070","https://openalex.org/W2136173754","https://openalex.org/W2062430949","https://openalex.org/W2110050003","https://openalex.org/W2953025626","https://openalex.org/W2499081552","https://openalex.org/W2366053282"],"abstract_inverted_index":{"Standard":[0],"necessary":[1],"conditions":[2,61,72],"for":[3,62],"optimal":[4],"control":[5],"problems":[6],"with":[7],"pathwise":[8],"state":[9,30,44,98,104,108],"constraints":[10],"supply":[11],"no":[12],"useful":[13],"information":[14],"about":[15],"minimizers":[16],"in":[17,39,47,111],"a":[18,50,96],"number":[19],"of":[20,22,29,42,56,65,70,92,95,103],"cases":[21,49],"interest,":[23],"e.g.,":[24],"when":[25],"the":[26,40,43,63,93,101,107,112],"left":[27],"endpoint":[28],"trajectories":[31,105],"is":[32,73],"fixed":[33],"at":[34],"x0":[35,37],"and":[36,80],"lies":[38],"boundary":[41],"constraint":[45],"set;":[46],"these":[48,71],"nonzero,":[51],"but":[52],"nevertheless":[53],"trivial,":[54],"set":[55,102],"multipliers":[57],"exists.":[58],"We":[59],"give":[60],"existence":[64],"nontrivial":[66],"multipliers.":[67],"A":[68],"feature":[69],"that":[74],"they":[75],"allow":[76],"nonconvex":[77],"velocity":[78],"sets":[79],"measurably":[81],"time-dependent":[82],"data.":[83],"The":[84],"proof":[85],"techniques":[86],"are":[87],"based":[88],"on":[89],"refined":[90],"estimates":[91],"distance":[94],"given":[97],"trajectory":[99],"from":[100],"satisfying":[106],"constraint,":[109],"originating":[110],"dynamic":[113],"programming":[114],"literature.":[115]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":3},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":5},{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":4},{"year":2012,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}