{"id":"https://openalex.org/W2070926313","doi":"https://doi.org/10.1137/s0363012901393304","title":"On the $\\lambda$-Equations for Matching Control Laws","display_name":"On the $\\lambda$-Equations for Matching Control Laws","publication_year":2002,"publication_date":"2002-01-01","ids":{"openalex":"https://openalex.org/W2070926313","doi":"https://doi.org/10.1137/s0363012901393304","mag":"2070926313"},"language":"en","primary_location":{"id":"doi:10.1137/s0363012901393304","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0363012901393304","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/A5111710655","display_name":"David Auckly","orcid":null},"institutions":[{"id":"https://openalex.org/I189590672","display_name":"Kansas State University","ror":"https://ror.org/05p1j8758","country_code":"US","type":"education","lineage":["https://openalex.org/I189590672"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"David Auckly","raw_affiliation_strings":["Kansas state university"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Kansas state university","institution_ids":["https://openalex.org/I189590672"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5065498086","display_name":"Lev Kapitanski","orcid":null},"institutions":[{"id":"https://openalex.org/I189590672","display_name":"Kansas State University","ror":"https://ror.org/05p1j8758","country_code":"US","type":"education","lineage":["https://openalex.org/I189590672"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Lev Kapitanski","raw_affiliation_strings":["Kansas state university"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Kansas state university","institution_ids":["https://openalex.org/I189590672"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I189590672"],"apc_list":null,"apc_paid":null,"fwci":8.912,"has_fulltext":false,"cited_by_count":79,"citation_normalized_percentile":{"value":0.97934037,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"41","issue":"5","first_page":"1372","last_page":"1388"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12772","display_name":"Control and Stability of Dynamical Systems","score":0.9997000098228455,"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/T12772","display_name":"Control and Stability of Dynamical Systems","score":0.9997000098228455,"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/T11110","display_name":"Stability and Controllability of Differential Equations","score":0.9850000143051147,"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/T11416","display_name":"Numerical methods for differential equations","score":0.9799000024795532,"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":0.7879685163497925},{"id":"https://openalex.org/keywords/matching","display_name":"Matching (statistics)","score":0.5796186327934265},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.564803957939148},{"id":"https://openalex.org/keywords/lambda","display_name":"Lambda","score":0.48727333545684814},{"id":"https://openalex.org/keywords/law","display_name":"Law","score":0.48143669962882996},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.42675361037254333},{"id":"https://openalex.org/keywords/degrees-of-freedom","display_name":"Degrees of freedom (physics and chemistry)","score":0.42515090107917786},{"id":"https://openalex.org/keywords/separable-partial-differential-equation","display_name":"Separable partial differential equation","score":0.4210744798183441},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3291088938713074},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.32502850890159607},{"id":"https://openalex.org/keywords/differential-algebraic-equation","display_name":"Differential algebraic equation","score":0.17036762833595276},{"id":"https://openalex.org/keywords/ordinary-differential-equation","display_name":"Ordinary differential equation","score":0.12765911221504211},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.06115061044692993}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7879685163497925},{"id":"https://openalex.org/C165064840","wikidata":"https://www.wikidata.org/wiki/Q1321061","display_name":"Matching (statistics)","level":2,"score":0.5796186327934265},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.564803957939148},{"id":"https://openalex.org/C2778113609","wikidata":"https://www.wikidata.org/wiki/Q10897","display_name":"Lambda","level":2,"score":0.48727333545684814},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.48143669962882996},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.42675361037254333},{"id":"https://openalex.org/C208081375","wikidata":"https://www.wikidata.org/wiki/Q274502","display_name":"Degrees of freedom (physics and chemistry)","level":2,"score":0.42515090107917786},{"id":"https://openalex.org/C101487385","wikidata":"https://www.wikidata.org/wiki/Q7451766","display_name":"Separable partial differential equation","level":5,"score":0.4210744798183441},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3291088938713074},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.32502850890159607},{"id":"https://openalex.org/C186219872","wikidata":"https://www.wikidata.org/wiki/Q955889","display_name":"Differential algebraic equation","level":4,"score":0.17036762833595276},{"id":"https://openalex.org/C51544822","wikidata":"https://www.wikidata.org/wiki/Q465274","display_name":"Ordinary differential equation","level":3,"score":0.12765911221504211},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.06115061044692993},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","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/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0},{"id":"https://openalex.org/C120665830","wikidata":"https://www.wikidata.org/wiki/Q14620","display_name":"Optics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/s0363012901393304","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0363012901393304","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"}],"best_oa_location":null,"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":12,"referenced_works":["https://openalex.org/W41860320","https://openalex.org/W1573190407","https://openalex.org/W1651729617","https://openalex.org/W1977165430","https://openalex.org/W2072770984","https://openalex.org/W2102263452","https://openalex.org/W2111185801","https://openalex.org/W2124863501","https://openalex.org/W2127198539","https://openalex.org/W2160979028","https://openalex.org/W2949659036","https://openalex.org/W2952218911"],"related_works":["https://openalex.org/W2088064134","https://openalex.org/W2083332431","https://openalex.org/W2479314534","https://openalex.org/W2042633045","https://openalex.org/W4386461811","https://openalex.org/W2029287765","https://openalex.org/W3035173621","https://openalex.org/W1991459776","https://openalex.org/W2969651353","https://openalex.org/W4295797339"],"abstract_inverted_index":{"We":[0,8,78,125],"discuss":[1],"matching":[2,15,86,108,115],"control":[3,16,87,116],"laws":[4,17,117],"for":[5,31,48,75],"underactuated":[6],"systems.":[7],"previously":[9],"showed":[10],"that":[11,70,101],"this":[12,132],"class":[13],"of":[14,25,34,42,52,66,85,99],"is":[18,92,133],"completely":[19],"characterized":[20],"by":[21,38],"a":[22,39,61,93,127],"linear":[23,40],"system":[24,41,65,94],"first":[26,43,63],"order":[27,44,64],"partial":[28,45,67],"differential":[29,46,68],"equations":[30,47,69],"one":[32],"set":[33,51],"variables":[35,53],"($\\,\\lambda$)":[36],"followed":[37],"the":[49,76,107,137],"second":[50],"($\\,{\\widehat":[54],"g}$,":[55],"$\\,{\\widehat":[56],"V}$).":[57],"Here":[58],"we":[59],"derive":[60],"new":[62],"encodes":[71],"all":[72],"compatibility":[73],"conditions":[74],"$\\,\\lambda$-equations.":[77],"give":[79],"four":[80],"examples":[81],"illustrating":[82],"different":[83],"features":[84],"laws.":[88],"The":[89],"last":[90],"example":[91],"with":[95,113],"two":[96],"unactuated":[97],"degrees":[98],"freedom":[100],"admits":[102],"only":[103,119],"basic":[104,120],"solutions":[105,121],"to":[106,135],"equations.":[109],"There":[110],"are":[111,122],"systems":[112],"many":[114],"where":[118],"potentially":[123],"useful.":[124],"introduce":[126],"rank":[128],"condition":[129],"indicating":[130],"when":[131],"likely":[134],"be":[136],"case.":[138]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":3},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":6},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":8},{"year":2012,"cited_by_count":9}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
