{"id":"https://openalex.org/W2145603256","doi":"https://doi.org/10.23919/acc.2004.1386807","title":"Discrete verification of necessary conditions for switched nonlinear optimal control systems","display_name":"Discrete verification of necessary conditions for switched nonlinear optimal control systems","publication_year":2004,"publication_date":"2004-01-01","ids":{"openalex":"https://openalex.org/W2145603256","doi":"https://doi.org/10.23919/acc.2004.1386807","mag":"2145603256"},"language":"en","primary_location":{"id":"doi:10.23919/acc.2004.1386807","is_oa":false,"landing_page_url":"https://doi.org/10.23919/acc.2004.1386807","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 2004 American Control Conference","raw_type":"proceedings-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/A5105125725","display_name":"Michael Ross","orcid":null},"institutions":[{"id":"https://openalex.org/I35364215","display_name":"Naval Postgraduate School","ror":"https://ror.org/033yfkj90","country_code":"US","type":"education","lineage":["https://openalex.org/I1330347796","https://openalex.org/I3130687028","https://openalex.org/I35364215"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"M.I. Ross","raw_affiliation_strings":["Department of Mechanical and Astronautical Engineering, Naval Postgraduate School, Monterrey, CA, USA","Dept. of Mech. & Astronaut. Eng., Naval Postgraduate Sch., Monterey, CA, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mechanical and Astronautical Engineering, Naval Postgraduate School, Monterrey, CA, USA","institution_ids":["https://openalex.org/I35364215"]},{"raw_affiliation_string":"Dept. of Mech. & Astronaut. Eng., Naval Postgraduate Sch., Monterey, CA, USA","institution_ids":["https://openalex.org/I35364215"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5110194286","display_name":"F. Fahroo","orcid":null},"institutions":[{"id":"https://openalex.org/I35364215","display_name":"Naval Postgraduate School","ror":"https://ror.org/033yfkj90","country_code":"US","type":"education","lineage":["https://openalex.org/I1330347796","https://openalex.org/I3130687028","https://openalex.org/I35364215"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"F. Fahroo","raw_affiliation_strings":["Department of Applied Mathematics, Naval Postgraduate School, Monterrey, CA, USA","Dept. of Mech. & Astronaut. Eng., Naval Postgraduate Sch., Monterey, CA, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics, Naval Postgraduate School, Monterrey, CA, USA","institution_ids":["https://openalex.org/I35364215"]},{"raw_affiliation_string":"Dept. of Mech. & Astronaut. Eng., Naval Postgraduate Sch., Monterey, CA, USA","institution_ids":["https://openalex.org/I35364215"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I35364215"],"apc_list":null,"apc_paid":null,"fwci":117.299,"has_fulltext":false,"cited_by_count":23,"citation_normalized_percentile":{"value":0.99853313,"is_in_top_1_percent":true,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":96},"biblio":{"volume":null,"issue":null,"first_page":"1610","last_page":"1615 vol.2"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11082","display_name":"Spacecraft Dynamics and Control","score":0.9980999827384949,"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"}},"topics":[{"id":"https://openalex.org/T11082","display_name":"Spacecraft Dynamics and Control","score":0.9980999827384949,"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":0.9955999851226807,"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/T10791","display_name":"Advanced Control Systems Optimization","score":0.9878000020980835,"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/discretization","display_name":"Discretization","score":0.834764838218689},{"id":"https://openalex.org/keywords/closure","display_name":"Closure (psychology)","score":0.5866477489471436},{"id":"https://openalex.org/keywords/lagrange-multiplier","display_name":"Lagrange multiplier","score":0.5686378479003906},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.5602657794952393},{"id":"https://openalex.org/keywords/optimal-control","display_name":"Optimal control","score":0.5412817001342773},{"id":"https://openalex.org/keywords/nonlinear-programming","display_name":"Nonlinear programming","score":0.5406138300895691},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5351648330688477},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.5235585570335388},{"id":"https://openalex.org/keywords/hybrid-system","display_name":"Hybrid system","score":0.501960039138794},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.4384559690952301},{"id":"https://openalex.org/keywords/state-variable","display_name":"State variable","score":0.4334031641483307},{"id":"https://openalex.org/keywords/state","display_name":"State (computer science)","score":0.4167999029159546},{"id":"https://openalex.org/keywords/optimization-problem","display_name":"Optimization problem","score":0.4130456745624542},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3928082585334778},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.23335573077201843},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.08738875389099121}],"concepts":[{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.834764838218689},{"id":"https://openalex.org/C146834321","wikidata":"https://www.wikidata.org/wiki/Q2979672","display_name":"Closure (psychology)","level":2,"score":0.5866477489471436},{"id":"https://openalex.org/C73684929","wikidata":"https://www.wikidata.org/wiki/Q598870","display_name":"Lagrange multiplier","level":2,"score":0.5686378479003906},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.5602657794952393},{"id":"https://openalex.org/C91575142","wikidata":"https://www.wikidata.org/wiki/Q1971426","display_name":"Optimal control","level":2,"score":0.5412817001342773},{"id":"https://openalex.org/C115527620","wikidata":"https://www.wikidata.org/wiki/Q769909","display_name":"Nonlinear programming","level":3,"score":0.5406138300895691},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5351648330688477},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.5235585570335388},{"id":"https://openalex.org/C50897621","wikidata":"https://www.wikidata.org/wiki/Q2665508","display_name":"Hybrid system","level":2,"score":0.501960039138794},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.4384559690952301},{"id":"https://openalex.org/C129537906","wikidata":"https://www.wikidata.org/wiki/Q7603913","display_name":"State variable","level":2,"score":0.4334031641483307},{"id":"https://openalex.org/C48103436","wikidata":"https://www.wikidata.org/wiki/Q599031","display_name":"State (computer science)","level":2,"score":0.4167999029159546},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.4130456745624542},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3928082585334778},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.23335573077201843},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.08738875389099121},{"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/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","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/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","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/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}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.23919/acc.2004.1386807","is_oa":false,"landing_page_url":"https://doi.org/10.23919/acc.2004.1386807","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 2004 American Control Conference","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/16","score":0.5,"display_name":"Peace, Justice and strong institutions"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":27,"referenced_works":["https://openalex.org/W601125530","https://openalex.org/W1513315067","https://openalex.org/W1514799972","https://openalex.org/W1528856837","https://openalex.org/W1530117215","https://openalex.org/W1583428626","https://openalex.org/W1603643961","https://openalex.org/W1805381866","https://openalex.org/W1960239420","https://openalex.org/W1982019931","https://openalex.org/W1985249384","https://openalex.org/W2002416438","https://openalex.org/W2018395639","https://openalex.org/W2020463339","https://openalex.org/W2029140461","https://openalex.org/W2039122122","https://openalex.org/W2101368332","https://openalex.org/W2119664948","https://openalex.org/W2129231075","https://openalex.org/W2137413756","https://openalex.org/W2149150807","https://openalex.org/W2152185829","https://openalex.org/W2153425320","https://openalex.org/W2187565700","https://openalex.org/W2341171179","https://openalex.org/W2798500587","https://openalex.org/W2798574506"],"related_works":["https://openalex.org/W2074745806","https://openalex.org/W1600454385","https://openalex.org/W1997033546","https://openalex.org/W3120556963","https://openalex.org/W1979241556","https://openalex.org/W2105377028","https://openalex.org/W4379919368","https://openalex.org/W2370558260","https://openalex.org/W3209065746","https://openalex.org/W2113133070"],"abstract_inverted_index":{"We":[0,40],"consider":[1],"a":[2,27,42,67,83,122],"fairly":[3],"general":[4],"class":[5],"of":[6,26,52,102,112,119,132],"state-constrained":[7],"nonlinear":[8],"hybrid":[9,97,123,148],"optimal":[10,149],"control":[11,150],"problems":[12],"that":[13,47,85,127],"are":[14,59,80,105],"based":[15],"on":[16],"coordinatizing":[17],"Sussmann's":[18],"model.":[19],"An":[20,116],"event":[21,57],"set":[22,33,101],"generalizes":[23],"the":[24,37,49,53,62,78,90,96,110,133,138,142,147],"notion":[25],"guard":[28],"set,":[29],"reset":[30],"map,":[31],"endpoint":[32],"as":[34,36],"well":[35],"switching":[38],"set.":[39],"present":[41],"pseudospectral":[43],"(PS)":[44],"knotting":[45],"method":[46],"discretizes":[48],"continuous-time":[50],"variables":[51],"problem.":[54,73,151],"The":[55,74],"discrete":[56],"conditions":[58,76,93,104],"imposed":[60],"over":[61],"PS":[63],"knots":[64],"leading":[65],"to":[66,107,141],"large,":[68],"sparse,":[69],"mixed-variable":[70],"programming":[71],"(MVP)":[72],"Karush-Kuhn-Tucker":[75],"for":[77],"MVP":[79],"transformed":[81],"in":[82],"manner":[84],"makes":[86],"them":[87],"closely":[88],"resemble":[89],"discretized":[91,139,143],"necessary":[92],"obtained":[94],"from":[95],"minimum":[98],"principle.":[99],"A":[100],"closure":[103],"introduced":[106],"facilitate":[108],"commuting":[109],"operations":[111],"dualization":[113],"and":[114],"discretization.":[115],"immediate":[117],"consequence":[118],"this":[120],"is":[121],"covector":[124],"mapping":[125],"theorem":[126],"provides":[128],"an":[129],"order-preserving":[130],"transformation":[131],"Lagrange":[134],"multipliers":[135],"associated":[136,145],"with":[137,146],"problem":[140],"covectors":[144]},"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":2},{"year":2012,"cited_by_count":1}],"updated_date":"2026-06-26T08:34:08.712188","created_date":"2025-10-10T00:00:00"}
