{"id":"https://openalex.org/W4313426555","doi":"https://doi.org/10.1109/lcsys.2022.3228723","title":"Contractivity of the Method of Successive Approximations for Optimal Control","display_name":"Contractivity of the Method of Successive Approximations for Optimal Control","publication_year":2022,"publication_date":"2022-12-13","ids":{"openalex":"https://openalex.org/W4313426555","doi":"https://doi.org/10.1109/lcsys.2022.3228723"},"language":"en","primary_location":{"id":"doi:10.1109/lcsys.2022.3228723","is_oa":false,"landing_page_url":"https://doi.org/10.1109/lcsys.2022.3228723","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/A5077158504","display_name":"Kevin Smith","orcid":"https://orcid.org/0000-0002-1407-5893"},"institutions":[{"id":"https://openalex.org/I154570441","display_name":"University of California, Santa Barbara","ror":"https://ror.org/02t274463","country_code":"US","type":"education","lineage":["https://openalex.org/I154570441"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Kevin D. Smith","raw_affiliation_strings":["Center for Control, Dynamical Systems, and Computation, University of California at Santa Barbara, Santa Barbara, CA, USA"],"raw_orcid":"https://orcid.org/0000-0002-1407-5893","affiliations":[{"raw_affiliation_string":"Center for Control, Dynamical Systems, and Computation, University of California at Santa Barbara, Santa Barbara, CA, USA","institution_ids":["https://openalex.org/I154570441"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5068353454","display_name":"Francesco Bullo","orcid":"https://orcid.org/0000-0002-4785-2118"},"institutions":[{"id":"https://openalex.org/I154570441","display_name":"University of California, Santa Barbara","ror":"https://ror.org/02t274463","country_code":"US","type":"education","lineage":["https://openalex.org/I154570441"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Francesco Bullo","raw_affiliation_strings":["Center for Control, Dynamical Systems, and Computation, University of California at Santa Barbara, Santa Barbara, CA, USA"],"raw_orcid":"https://orcid.org/0000-0002-4785-2118","affiliations":[{"raw_affiliation_string":"Center for Control, Dynamical Systems, and Computation, University of California at Santa Barbara, Santa Barbara, CA, USA","institution_ids":["https://openalex.org/I154570441"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.18049463,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"7","issue":null,"first_page":"919","last_page":"924"},"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":0.9998000264167786,"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":0.9998000264167786,"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/T11520","display_name":"Advanced Thermodynamics and Statistical Mechanics","score":0.994700014591217,"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/T11416","display_name":"Numerical methods for differential equations","score":0.9916999936103821,"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/pontryagins-minimum-principle","display_name":"Pontryagin's minimum principle","score":0.7844918966293335},{"id":"https://openalex.org/keywords/uniqueness","display_name":"Uniqueness","score":0.7101552486419678},{"id":"https://openalex.org/keywords/optimal-control","display_name":"Optimal control","score":0.6594837307929993},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5606750249862671},{"id":"https://openalex.org/keywords/simple","display_name":"Simple (philosophy)","score":0.556744396686554},{"id":"https://openalex.org/keywords/norm","display_name":"Norm (philosophy)","score":0.5437066555023193},{"id":"https://openalex.org/keywords/contraction-mapping","display_name":"Contraction mapping","score":0.5426024794578552},{"id":"https://openalex.org/keywords/dual","display_name":"Dual (grammatical number)","score":0.5386635065078735},{"id":"https://openalex.org/keywords/contraction","display_name":"Contraction (grammar)","score":0.5372296571731567},{"id":"https://openalex.org/keywords/rate-of-convergence","display_name":"Rate of convergence","score":0.5235235691070557},{"id":"https://openalex.org/keywords/dynamical-systems-theory","display_name":"Dynamical systems theory","score":0.5189142227172852},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4862314760684967},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.4836091101169586},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.4651407301425934},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.3797062635421753},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.3602406680583954},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3437731862068176},{"id":"https://openalex.org/keywords/mathematical-economics","display_name":"Mathematical economics","score":0.32182103395462036},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.23536145687103271},{"id":"https://openalex.org/keywords/economics","display_name":"Economics","score":0.16856148838996887},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.09513506293296814},{"id":"https://openalex.org/keywords/fixed-point","display_name":"Fixed point","score":0.08903840184211731},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.08541393280029297}],"concepts":[{"id":"https://openalex.org/C141803461","wikidata":"https://www.wikidata.org/wiki/Q3491629","display_name":"Pontryagin's minimum principle","level":3,"score":0.7844918966293335},{"id":"https://openalex.org/C2777021972","wikidata":"https://www.wikidata.org/wiki/Q22976830","display_name":"Uniqueness","level":2,"score":0.7101552486419678},{"id":"https://openalex.org/C91575142","wikidata":"https://www.wikidata.org/wiki/Q1971426","display_name":"Optimal control","level":2,"score":0.6594837307929993},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5606750249862671},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.556744396686554},{"id":"https://openalex.org/C191795146","wikidata":"https://www.wikidata.org/wiki/Q3878446","display_name":"Norm (philosophy)","level":2,"score":0.5437066555023193},{"id":"https://openalex.org/C55524764","wikidata":"https://www.wikidata.org/wiki/Q515173","display_name":"Contraction mapping","level":3,"score":0.5426024794578552},{"id":"https://openalex.org/C2780980858","wikidata":"https://www.wikidata.org/wiki/Q110022","display_name":"Dual (grammatical number)","level":2,"score":0.5386635065078735},{"id":"https://openalex.org/C163415756","wikidata":"https://www.wikidata.org/wiki/Q126473","display_name":"Contraction (grammar)","level":2,"score":0.5372296571731567},{"id":"https://openalex.org/C57869625","wikidata":"https://www.wikidata.org/wiki/Q1783502","display_name":"Rate of convergence","level":3,"score":0.5235235691070557},{"id":"https://openalex.org/C79379906","wikidata":"https://www.wikidata.org/wiki/Q3174497","display_name":"Dynamical systems theory","level":2,"score":0.5189142227172852},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4862314760684967},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.4836091101169586},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.4651407301425934},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.3797062635421753},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.3602406680583954},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3437731862068176},{"id":"https://openalex.org/C144237770","wikidata":"https://www.wikidata.org/wiki/Q747534","display_name":"Mathematical economics","level":1,"score":0.32182103395462036},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.23536145687103271},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.16856148838996887},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.09513506293296814},{"id":"https://openalex.org/C61445026","wikidata":"https://www.wikidata.org/wiki/Q217608","display_name":"Fixed point","level":2,"score":0.08903840184211731},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.08541393280029297},{"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/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","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/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0},{"id":"https://openalex.org/C31258907","wikidata":"https://www.wikidata.org/wiki/Q1301371","display_name":"Computer network","level":1,"score":0.0},{"id":"https://openalex.org/C126322002","wikidata":"https://www.wikidata.org/wiki/Q11180","display_name":"Internal medicine","level":1,"score":0.0},{"id":"https://openalex.org/C142362112","wikidata":"https://www.wikidata.org/wiki/Q735","display_name":"Art","level":0,"score":0.0},{"id":"https://openalex.org/C124952713","wikidata":"https://www.wikidata.org/wiki/Q8242","display_name":"Literature","level":1,"score":0.0},{"id":"https://openalex.org/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","level":0,"score":0.0},{"id":"https://openalex.org/C127162648","wikidata":"https://www.wikidata.org/wiki/Q16858953","display_name":"Channel (broadcasting)","level":2,"score":0.0},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/lcsys.2022.3228723","is_oa":false,"landing_page_url":"https://doi.org/10.1109/lcsys.2022.3228723","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/G3055473026","display_name":null,"funder_award_id":"FA9550-21-1-0203","funder_id":"https://openalex.org/F4320338279","funder_display_name":"Air Force Office of Scientific Research"},{"id":"https://openalex.org/G6688516561","display_name":null,"funder_award_id":"FA9550-22-1-0059","funder_id":"https://openalex.org/F4320338279","funder_display_name":"Air Force Office of Scientific Research"}],"funders":[{"id":"https://openalex.org/F4320338279","display_name":"Air Force Office of Scientific Research","ror":"https://ror.org/011e9bt93"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":22,"referenced_works":["https://openalex.org/W231975775","https://openalex.org/W246300151","https://openalex.org/W283036238","https://openalex.org/W1510003436","https://openalex.org/W2007770288","https://openalex.org/W2035670438","https://openalex.org/W2035904219","https://openalex.org/W2059359356","https://openalex.org/W2063917507","https://openalex.org/W2102884619","https://openalex.org/W2135404129","https://openalex.org/W2221321873","https://openalex.org/W2600297185","https://openalex.org/W2765410998","https://openalex.org/W3031802121","https://openalex.org/W3207782042","https://openalex.org/W4206582666","https://openalex.org/W4212774754","https://openalex.org/W4285262316","https://openalex.org/W6744834936","https://openalex.org/W6749720326","https://openalex.org/W6762775584"],"related_works":["https://openalex.org/W2962746246","https://openalex.org/W1967384683","https://openalex.org/W4292923857","https://openalex.org/W4285534277","https://openalex.org/W162218241","https://openalex.org/W3031081244","https://openalex.org/W4302321938","https://openalex.org/W3209004265","https://openalex.org/W1643670820","https://openalex.org/W2208523677"],"abstract_inverted_index":{"Strongly":[0],"contracting":[1,36],"dynamical":[2,40],"systems":[3],"have":[4],"numerous":[5],"properties":[6],"(e.g.,":[7,13],"incremental":[8],"ISS),":[9],"find":[10],"widespread":[11],"applications":[12],"in":[14,79],"controls":[15],"and":[16,18,112],"learning),":[17],"their":[19],"study":[20],"is":[21,42,82],"receiving":[22],"increasing":[23],"attention.":[24],"This":[25],"letter":[26],"starts":[27],"with":[28,46,50],"the":[29,47,53,69,101,109],"simple":[30],"observation":[31],"that,":[32],"given":[33],"a":[34,83],"strongly":[35,44],"system,":[37],"its":[38],"adjoint":[39],"system":[41],"also":[43],"contracting,":[45],"same":[48],"rate,":[49],"respect":[51],"to":[52],"dual":[54,64],"norm,":[55],"under":[56,118],"time":[57],"reversal.":[58],"As":[59],"main":[60],"implication":[61],"of":[62,72,108,114],"this":[63],"contractivity,":[65],"we":[66,95],"show":[67],"that":[68],"classic":[70],"Method":[71],"Successive":[73],"Approximations":[74],"(MSA),":[75],"an":[76],"indirect":[77],"method":[78],"optimal":[80,110],"control,":[81],"contraction":[84,92],"mapping":[85],"for":[86,100],"short":[87],"optimization":[88],"intervals":[89],"or":[90],"large":[91],"rates.":[93],"Consequently,":[94],"establish":[96],"new":[97],"convergence":[98],"conditions":[99],"MSA":[102],"algorithm,":[103],"which":[104],"further":[105],"imply":[106],"uniqueness":[107],"control":[111],"sufficiency":[113],"Pontryagin\u2019s":[115],"minimum":[116],"principle":[117],"additional":[119],"assumptions.":[120]},"counts_by_year":[],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}
