{"id":"https://openalex.org/W1149645490","doi":"https://doi.org/10.1137/14099440x","title":"Regularity of the Hamiltonian Along Optimal Trajectories","display_name":"Regularity of the Hamiltonian Along Optimal Trajectories","publication_year":2015,"publication_date":"2015-01-01","ids":{"openalex":"https://openalex.org/W1149645490","doi":"https://doi.org/10.1137/14099440x","mag":"1149645490"},"language":"en","primary_location":{"id":"doi:10.1137/14099440x","is_oa":false,"landing_page_url":"https://doi.org/10.1137/14099440x","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":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1912.11863","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"M. Palladino","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"M. Palladino","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":null,"display_name":"R. B. Vinter","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"R. B. Vinter","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":2.04,"has_fulltext":false,"cited_by_count":12,"citation_normalized_percentile":{"value":0.86760394,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"53","issue":"4","first_page":"1892","last_page":"1919"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10545","display_name":"Optimization and Variational Analysis","score":0.7878999710083008,"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":0.7878999710083008,"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/T11082","display_name":"Spacecraft Dynamics and Control","score":0.09470000118017197,"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/T12772","display_name":"Control and Stability of Dynamical Systems","score":0.02370000071823597,"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/differential-inclusion","display_name":"Differential inclusion","score":0.909600019454956},{"id":"https://openalex.org/keywords/lipschitz-continuity","display_name":"Lipschitz continuity","score":0.8510000109672546},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.7727000117301941},{"id":"https://openalex.org/keywords/trajectory","display_name":"Trajectory","score":0.5796999931335449},{"id":"https://openalex.org/keywords/optimal-control","display_name":"Optimal control","score":0.5776000022888184},{"id":"https://openalex.org/keywords/bounded-variation","display_name":"Bounded variation","score":0.5501000285148621},{"id":"https://openalex.org/keywords/hamiltonian","display_name":"Hamiltonian (control theory)","score":0.4893999993801117},{"id":"https://openalex.org/keywords/state","display_name":"State (computer science)","score":0.4738999903202057},{"id":"https://openalex.org/keywords/differential","display_name":"Differential (mechanical device)","score":0.424699991941452}],"concepts":[{"id":"https://openalex.org/C70834904","wikidata":"https://www.wikidata.org/wiki/Q1054638","display_name":"Differential inclusion","level":2,"score":0.909600019454956},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8616999983787537},{"id":"https://openalex.org/C22324862","wikidata":"https://www.wikidata.org/wiki/Q652707","display_name":"Lipschitz continuity","level":2,"score":0.8510000109672546},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.7727000117301941},{"id":"https://openalex.org/C13662910","wikidata":"https://www.wikidata.org/wiki/Q193139","display_name":"Trajectory","level":2,"score":0.5796999931335449},{"id":"https://openalex.org/C91575142","wikidata":"https://www.wikidata.org/wiki/Q1971426","display_name":"Optimal control","level":2,"score":0.5776000022888184},{"id":"https://openalex.org/C27851653","wikidata":"https://www.wikidata.org/wiki/Q829653","display_name":"Bounded variation","level":2,"score":0.5501000285148621},{"id":"https://openalex.org/C130787639","wikidata":"https://www.wikidata.org/wiki/Q5645293","display_name":"Hamiltonian (control theory)","level":2,"score":0.4893999993801117},{"id":"https://openalex.org/C48103436","wikidata":"https://www.wikidata.org/wiki/Q599031","display_name":"State (computer science)","level":2,"score":0.4738999903202057},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.43950000405311584},{"id":"https://openalex.org/C93226319","wikidata":"https://www.wikidata.org/wiki/Q193137","display_name":"Differential (mechanical device)","level":2,"score":0.424699991941452},{"id":"https://openalex.org/C147764199","wikidata":"https://www.wikidata.org/wiki/Q6865248","display_name":"Minification","level":2,"score":0.3720000088214874},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3610000014305115},{"id":"https://openalex.org/C51544822","wikidata":"https://www.wikidata.org/wiki/Q465274","display_name":"Ordinary differential equation","level":3,"score":0.35499998927116394},{"id":"https://openalex.org/C2776036281","wikidata":"https://www.wikidata.org/wiki/Q48769818","display_name":"Constraint (computer-aided design)","level":2,"score":0.35040000081062317},{"id":"https://openalex.org/C2984679396","wikidata":"https://www.wikidata.org/wiki/Q7602986","display_name":"State dependent","level":2,"score":0.3091000020503998},{"id":"https://openalex.org/C129537906","wikidata":"https://www.wikidata.org/wiki/Q7603913","display_name":"State variable","level":2,"score":0.30239999294281006},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.30140000581741333},{"id":"https://openalex.org/C31010330","wikidata":"https://www.wikidata.org/wiki/Q1914255","display_name":"Maximum principle","level":3,"score":0.29809999465942383},{"id":"https://openalex.org/C90377204","wikidata":"https://www.wikidata.org/wiki/Q1052594","display_name":"Uniform boundedness","level":3,"score":0.2888999879360199},{"id":"https://openalex.org/C121770821","wikidata":"https://www.wikidata.org/wiki/Q2072471","display_name":"Hamiltonian system","level":2,"score":0.2872999906539917},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.2840000092983246},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.27309998869895935},{"id":"https://openalex.org/C136005978","wikidata":"https://www.wikidata.org/wiki/Q1362077","display_name":"First variation","level":2,"score":0.27090001106262207},{"id":"https://openalex.org/C2779006483","wikidata":"https://www.wikidata.org/wiki/Q1973196","display_name":"Differential game","level":2,"score":0.26190000772476196},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.2597000002861023},{"id":"https://openalex.org/C26955809","wikidata":"https://www.wikidata.org/wiki/Q10167591","display_name":"Initial value problem","level":2,"score":0.25780001282691956}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1137/14099440x","is_oa":false,"landing_page_url":"https://doi.org/10.1137/14099440x","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:arXiv.org:1912.11863","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1912.11863","pdf_url":"https://arxiv.org/pdf/1912.11863","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"pmh:oai:spiral.imperial.ac.uk:10044/1/40469","is_oa":false,"landing_page_url":"http://hdl.handle.net/10044/1/40469","pdf_url":null,"source":{"id":"https://openalex.org/S4306401396","display_name":"Spiral (Imperial College London)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I47508984","host_organization_name":"Imperial College London","host_organization_lineage":["https://openalex.org/I47508984"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"1919","raw_type":"Journal Article"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1912.11863","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1912.11863","pdf_url":"https://arxiv.org/pdf/1912.11863","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1823500649","display_name":null,"funder_award_id":"EP/G066477/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"}],"funders":[{"id":"https://openalex.org/F4320334627","display_name":"Engineering and Physical Sciences Research Council","ror":"https://ror.org/0439y7842"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":12,"referenced_works":["https://openalex.org/W1487326569","https://openalex.org/W1970735217","https://openalex.org/W1976930521","https://openalex.org/W1983536992","https://openalex.org/W1983939399","https://openalex.org/W1991358247","https://openalex.org/W2001405973","https://openalex.org/W2051552175","https://openalex.org/W2069746992","https://openalex.org/W2123354485","https://openalex.org/W2132325680","https://openalex.org/W2913332731"],"related_works":[],"abstract_inverted_index":{"This":[0],"paper":[1],"concerns":[2],"state":[3,36,60,85,131,227],"constrained":[4],"optimal":[5,35,59,84,130],"control":[6],"problems,":[7],"in":[8,164,182,211,221],"which":[9,155,180,212],"the":[10,14,21,30,34,39,47,54,58,63,76,79,83,88,92,96,116,125,129,134,157,165,183,208,217],"dynamic":[11],"constraint":[12],"takes":[13],"form":[15,166],"of":[16,44,75,95,113,142,159,162,167,185,200,224],"a":[17,168,195,222,225],"differential":[18,22,48,97,117,201],"inclusion.":[19,170],"If":[20,46],"inclusion":[23,49,118],"does":[24],"not":[25],"depend":[26],"on":[27,194,216],"time,":[28,123],"then":[29,53,124],"Hamiltonian,":[31,55,80,126],"evaluated":[32,56,81,127],"along":[33,57,82,128],"trajectory":[37,61,86,132],"and":[38,62,87,133],"co-state":[40,64,89,135],"trajectory,":[41,65,90,136],"is":[42,50,66,150,174,192],"independent":[43],"time.":[45],"Lipschitz":[51,67],"continuous,":[52],"continuous.":[68],"These":[69],"two":[70],"well-known":[71],"results":[72],"are":[73,147,214],"examples":[74],"following":[77],"principle:":[78],"inherits":[91],"regularity":[93],"properties":[94,146],"inclusion,":[98],"regarding":[99],"its":[100],"time":[101,209],"dependence.":[102],"We":[103],"show":[104],"that":[105,203],"this":[106],"principle":[107],"also":[108],"applies":[109],"to":[110,151,175],"another":[111],"kind":[112],"regularity:":[114],"if":[115],"has":[119,137],"bounded":[120,138,188,205],"variation":[121,206],"w.r.t.":[122,207],"variation.":[139],"Two":[140],"applications":[141],"these":[143],"newly":[144],"found":[145],"demonstrated.":[148],"One":[149],"derive":[152,176],"improved":[153],"conditions":[154,161,178,213],"guarantee":[156],"nondegeneracy":[158],"necessary":[160],"optimality":[163],"Hamiltonian":[169],"The":[171,190],"other":[172],"application":[173],"new":[177],"under":[179],"minimizers":[181],"calculus":[184],"variations":[186],"have":[187,204],"slope.":[189],"analysis":[191],"based":[193],"recently":[196],"proposed,":[197],"local":[198],"concept":[199],"inclusions":[202],"variable,":[210],"imposed":[215],"multifunction":[218],"involved,":[219],"only":[220],"neighborhood":[223],"given":[226],"trajectory.":[228]},"counts_by_year":[{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":3},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":1}],"updated_date":"2026-08-26T07:47:46.906454","created_date":"2016-06-24T00:00:00"}