{"id":"https://openalex.org/W2579947342","doi":"https://doi.org/10.1137/16m1091654","title":"Optimal Control Problems with Symmetry Breaking Cost Functions","display_name":"Optimal Control Problems with Symmetry Breaking Cost Functions","publication_year":2017,"publication_date":"2017-01-01","ids":{"openalex":"https://openalex.org/W2579947342","doi":"https://doi.org/10.1137/16m1091654","mag":"2579947342"},"language":"en","primary_location":{"id":"doi:10.1137/16m1091654","is_oa":false,"landing_page_url":"https://doi.org/10.1137/16m1091654","pdf_url":null,"source":{"id":"https://openalex.org/S2996807011","display_name":"SIAM Journal on Applied Algebra and Geometry","issn_l":"2470-6566","issn":["2470-6566"],"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 Applied Algebra and Geometry","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/A5105787826","display_name":"Anthony M. Bloch","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Anthony M. Bloch","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5011498718","display_name":"Leonardo Colombo","orcid":"https://orcid.org/0000-0003-2085-3871"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Leonardo J. Colombo","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5053349247","display_name":"Rohit Gupta","orcid":"https://orcid.org/0000-0002-5873-7510"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Rohit Gupta","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5082931316","display_name":"Tomoki Ohsawa","orcid":"https://orcid.org/0000-0001-9406-132X"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Tomoki Ohsawa","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5105787826"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":2.4809,"has_fulltext":false,"cited_by_count":12,"citation_normalized_percentile":{"value":0.88334924,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":97},"biblio":{"volume":"1","issue":"1","first_page":"626","last_page":"646"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11416","display_name":"Numerical methods for differential equations","score":0.9872999787330627,"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"}},"topics":[{"id":"https://openalex.org/T11416","display_name":"Numerical methods for differential equations","score":0.9872999787330627,"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"}},{"id":"https://openalex.org/T10040","display_name":"Adaptive Control of Nonlinear Systems","score":0.9782000184059143,"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/T11394","display_name":"Dynamics and Control of Mechanical Systems","score":0.9769999980926514,"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/legendre-transformation","display_name":"Legendre transformation","score":0.685928463935852},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6647894382476807},{"id":"https://openalex.org/keywords/optimal-control","display_name":"Optimal control","score":0.5875084400177002},{"id":"https://openalex.org/keywords/affine-transformation","display_name":"Affine transformation","score":0.5274819731712341},{"id":"https://openalex.org/keywords/invariant","display_name":"Invariant (physics)","score":0.4650168716907501},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.44146841764450073},{"id":"https://openalex.org/keywords/context","display_name":"Context (archaeology)","score":0.4394649565219879},{"id":"https://openalex.org/keywords/variational-principle","display_name":"Variational principle","score":0.4236985743045807},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3118038773536682},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3059096932411194},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.17296871542930603},{"id":"https://openalex.org/keywords/mathematical-physics","display_name":"Mathematical physics","score":0.12350884079933167}],"concepts":[{"id":"https://openalex.org/C116594300","wikidata":"https://www.wikidata.org/wiki/Q908652","display_name":"Legendre transformation","level":2,"score":0.685928463935852},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6647894382476807},{"id":"https://openalex.org/C91575142","wikidata":"https://www.wikidata.org/wiki/Q1971426","display_name":"Optimal control","level":2,"score":0.5875084400177002},{"id":"https://openalex.org/C92757383","wikidata":"https://www.wikidata.org/wiki/Q382497","display_name":"Affine transformation","level":2,"score":0.5274819731712341},{"id":"https://openalex.org/C190470478","wikidata":"https://www.wikidata.org/wiki/Q2370229","display_name":"Invariant (physics)","level":2,"score":0.4650168716907501},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.44146841764450073},{"id":"https://openalex.org/C2779343474","wikidata":"https://www.wikidata.org/wiki/Q3109175","display_name":"Context (archaeology)","level":2,"score":0.4394649565219879},{"id":"https://openalex.org/C9259290","wikidata":"https://www.wikidata.org/wiki/Q745215","display_name":"Variational principle","level":2,"score":0.4236985743045807},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3118038773536682},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3059096932411194},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.17296871542930603},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.12350884079933167},{"id":"https://openalex.org/C151730666","wikidata":"https://www.wikidata.org/wiki/Q7205","display_name":"Paleontology","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/16m1091654","is_oa":false,"landing_page_url":"https://doi.org/10.1137/16m1091654","pdf_url":null,"source":{"id":"https://openalex.org/S2996807011","display_name":"SIAM Journal on Applied Algebra and Geometry","issn_l":"2470-6566","issn":["2470-6566"],"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 Applied Algebra and Geometry","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/11","display_name":"Sustainable cities and communities","score":0.6000000238418579}],"awards":[{"id":"https://openalex.org/G5134391561","display_name":null,"funder_award_id":"MTM 2013-42870-P","funder_id":"https://openalex.org/F4320321837","funder_display_name":"Ministerio de Econom\u00eda y Competitividad"},{"id":"https://openalex.org/G6729330135","display_name":null,"funder_award_id":"DMS-1613819","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G6843788055","display_name":null,"funder_award_id":"INSPIRE-1343720","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G8466983303","display_name":null,"funder_award_id":"DMS-1207693","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320306164","display_name":"Simons Foundation","ror":"https://ror.org/01cmst727"},{"id":"https://openalex.org/F4320321837","display_name":"Ministerio de Econom\u00eda y Competitividad","ror":"https://ror.org/034900433"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":29,"referenced_works":["https://openalex.org/W1495727713","https://openalex.org/W1542190445","https://openalex.org/W1595765050","https://openalex.org/W1810841586","https://openalex.org/W1841697596","https://openalex.org/W1979251648","https://openalex.org/W1982779826","https://openalex.org/W1987334278","https://openalex.org/W1993300073","https://openalex.org/W1999111109","https://openalex.org/W1999726309","https://openalex.org/W2008796127","https://openalex.org/W2014613771","https://openalex.org/W2020681603","https://openalex.org/W2046996497","https://openalex.org/W2047942475","https://openalex.org/W2059136277","https://openalex.org/W2082280760","https://openalex.org/W2083802218","https://openalex.org/W2101341777","https://openalex.org/W2119135605","https://openalex.org/W2132849333","https://openalex.org/W2155700785","https://openalex.org/W2162550557","https://openalex.org/W2171658097","https://openalex.org/W2176623737","https://openalex.org/W2501142942","https://openalex.org/W2551354800","https://openalex.org/W3099794008"],"related_works":["https://openalex.org/W3099466340","https://openalex.org/W2461927677","https://openalex.org/W2262841177","https://openalex.org/W2048571799","https://openalex.org/W1991332319","https://openalex.org/W1662693615","https://openalex.org/W3008890229","https://openalex.org/W3121596904","https://openalex.org/W3115114232","https://openalex.org/W2302532851"],"abstract_inverted_index":{"We":[0,96,110],"investigate":[1],"symmetry":[2,18,57],"reduction":[3],"of":[4,27,126],"optimal":[5,46],"control":[6,10,47],"problems":[7],"for":[8],"left-invariant":[9],"affine":[11],"systems":[12],"on":[13],"Lie":[14],"groups,":[15],"with":[16,54,114],"partial":[17,56],"breaking":[19,58],"cost":[20],"functions.":[21],"Our":[22],"approach":[23],"emphasizes":[24],"the":[25,38,45,62,76,93,99,106,112,124],"role":[26],"variational":[28,52,67,100],"principles":[29],"and":[30,60,82,104],"considers":[31],"a":[32,50,55,66,71,119],"discrete-time":[33,107],"setting":[34],"as":[35,37,49],"well":[36],"standard":[39],"continuous-time":[40],"formulation.":[41],"Specifically,":[42],"we":[43,74],"recast":[44],"problem":[48,53,122],"constrained":[51],"Lagrangian":[59],"obtain":[61,105],"Euler--Poincar\u00e9":[63],"equations":[64,78],"from":[65],"principle.":[68],"By":[69],"using":[70],"Legendre":[72],"transformation,":[73],"recover":[75],"Lie--Poisson":[77,108],"obtained":[79],"by":[80],"Borum":[81],"Bretl":[83],"[IEEE":[84],"Trans.":[85],"Automat.":[86],"Control,":[87],"62":[88],"(2017),":[89],"pp.":[90],"3209--3224]":[91],"in":[92,102,123],"same":[94],"context.":[95],"also":[97],"discretize":[98],"principle":[101],"time":[103],"equations.":[109],"illustrate":[111],"theory":[113],"some":[115],"practical":[116],"examples":[117],"including":[118],"motion":[120],"planning":[121],"presence":[125],"an":[127],"obstacle.":[128]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":3},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":3},{"year":2017,"cited_by_count":1}],"updated_date":"2026-06-05T09:01:59.212387","created_date":"2025-10-10T00:00:00"}