{"id":"https://openalex.org/W3203556267","doi":"https://doi.org/10.1080/00207179.2021.1986232","title":"A different look at the optimal control of the Brockett integrator","display_name":"A different look at the optimal control of the Brockett integrator","publication_year":2021,"publication_date":"2021-09-28","ids":{"openalex":"https://openalex.org/W3203556267","doi":"https://doi.org/10.1080/00207179.2021.1986232","mag":"3203556267"},"language":"en","primary_location":{"id":"doi:10.1080/00207179.2021.1986232","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207179.2021.1986232","pdf_url":null,"source":{"id":"https://openalex.org/S88061139","display_name":"International Journal of Control","issn_l":"0020-7179","issn":["0020-7179","1366-5820"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Control","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/A5008152552","display_name":"Domenico D\u2019Alessandro","orcid":"https://orcid.org/0000-0003-0179-7157"},"institutions":[{"id":"https://openalex.org/I173911158","display_name":"Iowa State University","ror":"https://ror.org/04rswrd78","country_code":"US","type":"education","lineage":["https://openalex.org/I173911158"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Domenico D'Alessandro","raw_affiliation_strings":["Department of Mathematics, Iowa State University, Ames, IA, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Iowa State University, Ames, IA, USA","institution_ids":["https://openalex.org/I173911158"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5047451408","display_name":"Zhifei Zhu","orcid":"https://orcid.org/0000-0002-1381-2804"},"institutions":[{"id":"https://openalex.org/I173911158","display_name":"Iowa State University","ror":"https://ror.org/04rswrd78","country_code":"US","type":"education","lineage":["https://openalex.org/I173911158"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Zhifei Zhu","raw_affiliation_strings":["Department of Mathematics, Iowa State University, Ames, IA, USA"],"raw_orcid":"https://orcid.org/0000-0002-1381-2804","affiliations":[{"raw_affiliation_string":"Department of Mathematics, Iowa State University, Ames, IA, USA","institution_ids":["https://openalex.org/I173911158"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5047451408"],"corresponding_institution_ids":["https://openalex.org/I173911158"],"apc_list":null,"apc_paid":null,"fwci":0.1388,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.4607154,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"96","issue":"1","first_page":"191","last_page":"200"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11615","display_name":"Control and Dynamics of Mobile Robots","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/T11615","display_name":"Control and Dynamics of Mobile Robots","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/T13080","display_name":"Advanced Differential Geometry Research","score":0.9850000143051147,"subfield":{"id":"https://openalex.org/subfields/3103","display_name":"Astronomy and Astrophysics"},"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/T12396","display_name":"Advanced Differential Equations and Dynamical Systems","score":0.9710000157356262,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"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":0.8234833478927612},{"id":"https://openalex.org/keywords/geodesic","display_name":"Geodesic","score":0.8181614875793457},{"id":"https://openalex.org/keywords/nonholonomic-system","display_name":"Nonholonomic system","score":0.6643689274787903},{"id":"https://openalex.org/keywords/quotient","display_name":"Quotient","score":0.6105024814605713},{"id":"https://openalex.org/keywords/metric","display_name":"Metric (unit)","score":0.5287688970565796},{"id":"https://openalex.org/keywords/integrator","display_name":"Integrator","score":0.4702538251876831},{"id":"https://openalex.org/keywords/space","display_name":"Space (punctuation)","score":0.4574441611766815},{"id":"https://openalex.org/keywords/symmetry","display_name":"Symmetry (geometry)","score":0.44727402925491333},{"id":"https://openalex.org/keywords/optimal-control","display_name":"Optimal control","score":0.41047403216362},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.39176836609840393},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.35261356830596924},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3280787467956543},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.1376504898071289},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.12624511122703552},{"id":"https://openalex.org/keywords/mobile-robot","display_name":"Mobile robot","score":0.10652229189872742},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.09967190027236938}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8234833478927612},{"id":"https://openalex.org/C165818556","wikidata":"https://www.wikidata.org/wiki/Q213488","display_name":"Geodesic","level":2,"score":0.8181614875793457},{"id":"https://openalex.org/C138632511","wikidata":"https://www.wikidata.org/wiki/Q2478109","display_name":"Nonholonomic system","level":4,"score":0.6643689274787903},{"id":"https://openalex.org/C199422724","wikidata":"https://www.wikidata.org/wiki/Q41118","display_name":"Quotient","level":2,"score":0.6105024814605713},{"id":"https://openalex.org/C176217482","wikidata":"https://www.wikidata.org/wiki/Q860554","display_name":"Metric (unit)","level":2,"score":0.5287688970565796},{"id":"https://openalex.org/C79518650","wikidata":"https://www.wikidata.org/wiki/Q2081431","display_name":"Integrator","level":3,"score":0.4702538251876831},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.4574441611766815},{"id":"https://openalex.org/C2779886137","wikidata":"https://www.wikidata.org/wiki/Q21030012","display_name":"Symmetry (geometry)","level":2,"score":0.44727402925491333},{"id":"https://openalex.org/C91575142","wikidata":"https://www.wikidata.org/wiki/Q1971426","display_name":"Optimal control","level":2,"score":0.41047403216362},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.39176836609840393},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.35261356830596924},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3280787467956543},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.1376504898071289},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.12624511122703552},{"id":"https://openalex.org/C19966478","wikidata":"https://www.wikidata.org/wiki/Q4810574","display_name":"Mobile robot","level":3,"score":0.10652229189872742},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.09967190027236938},{"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/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C90509273","wikidata":"https://www.wikidata.org/wiki/Q11012","display_name":"Robot","level":2,"score":0.0},{"id":"https://openalex.org/C21547014","wikidata":"https://www.wikidata.org/wiki/Q1423657","display_name":"Operations management","level":1,"score":0.0},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0},{"id":"https://openalex.org/C2776257435","wikidata":"https://www.wikidata.org/wiki/Q1576430","display_name":"Bandwidth (computing)","level":2,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1080/00207179.2021.1986232","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207179.2021.1986232","pdf_url":null,"source":{"id":"https://openalex.org/S88061139","display_name":"International Journal of Control","issn_l":"0020-7179","issn":["0020-7179","1366-5820"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Control","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.8399999737739563,"display_name":"Affordable and clean energy","id":"https://metadata.un.org/sdg/7"}],"awards":[{"id":"https://openalex.org/G6345927703","display_name":null,"funder_award_id":"ECCS 1710558","funder_id":"https://openalex.org/F4320337380","funder_display_name":"Division of Mathematical Sciences"}],"funders":[{"id":"https://openalex.org/F4320337380","display_name":"Division of Mathematical Sciences","ror":"https://ror.org/051fftw81"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":24,"referenced_works":["https://openalex.org/W22545347","https://openalex.org/W1515066108","https://openalex.org/W1564897360","https://openalex.org/W1574226641","https://openalex.org/W1849832765","https://openalex.org/W1971044547","https://openalex.org/W1971093859","https://openalex.org/W1983145721","https://openalex.org/W1987334278","https://openalex.org/W1991332019","https://openalex.org/W2006725138","https://openalex.org/W2047942475","https://openalex.org/W2062076432","https://openalex.org/W2101003581","https://openalex.org/W2133361850","https://openalex.org/W2942391093","https://openalex.org/W2963565741","https://openalex.org/W2966911517","https://openalex.org/W3099794008","https://openalex.org/W3099919989","https://openalex.org/W3104319045","https://openalex.org/W4206033904","https://openalex.org/W4210956211","https://openalex.org/W4248613038"],"related_works":["https://openalex.org/W2498988072","https://openalex.org/W2963456550","https://openalex.org/W2380347753","https://openalex.org/W4249580765","https://openalex.org/W2083558857","https://openalex.org/W2885318960","https://openalex.org/W1506668851","https://openalex.org/W2087561891","https://openalex.org/W4289123087","https://openalex.org/W2905154241"],"abstract_inverted_index":{"We":[0],"propose":[1],"a":[2,44,65],"method":[3,49],"to":[4,16,40,77,86],"analyze":[5],"the":[6,12,18,35,57,62,72,82,87,93,97],"three-dimensional":[7],"nonholonomic":[8,29],"system":[9],"known":[10],"as":[11],"Brockett":[13],"integrator":[14],"and":[15,53],"derive":[17,92],"(energy)":[19],"optimal":[20,37,94],"trajectories":[21,38,95],"between":[22],"two":[23],"given":[24],"points.":[25],"For":[26],"systems":[27],"with":[28,61,75],"constraint,":[30],"it":[31],"is":[32],"well-known":[33],"that":[34],"energy":[36],"corresponds":[39],"sub-Riemannian":[41,46],"geodesics":[42,74],"under":[43],"proper":[45],"metric.":[47],"Our":[48],"uses":[50],"symmetry":[51],"reduction":[52],"an":[54,78],"analysis":[55],"of":[56,64,96],"quotient":[58,83],"space":[59,84,89],"associated":[60],"action":[63],"(symmetry)":[66],"group":[67],"on":[68],"R3.":[69],"By":[70],"lifting":[71],"Riemannian":[73],"respect":[76],"appropriate":[79],"metric":[80],"from":[81],"back":[85],"original":[88,98],"R3,":[90],"we":[91],"problem.":[99]},"counts_by_year":[{"year":2024,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}