{"id":"https://openalex.org/W4385444301","doi":"https://doi.org/10.23919/ecc57647.2023.10178181","title":"Direct Collocation for Numerical Optimal Control of Second-Order ODE","display_name":"Direct Collocation for Numerical Optimal Control of Second-Order ODE","publication_year":2023,"publication_date":"2023-06-13","ids":{"openalex":"https://openalex.org/W4385444301","doi":"https://doi.org/10.23919/ecc57647.2023.10178181"},"language":"en","primary_location":{"id":"doi:10.23919/ecc57647.2023.10178181","is_oa":false,"landing_page_url":"http://dx.doi.org/10.23919/ecc57647.2023.10178181","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2023 European Control Conference (ECC)","raw_type":"proceedings-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/A5081175634","display_name":"L\u00e9o Simpson","orcid":null},"institutions":[{"id":"https://openalex.org/I136150977","display_name":"TE Connectivity (Switzerland)","ror":"https://ror.org/05he43612","country_code":"CH","type":"company","lineage":["https://openalex.org/I136150977"]}],"countries":["CH"],"is_corresponding":true,"raw_author_name":"L\u00e9o Simpson","raw_affiliation_strings":["Research and Development team, Tool-Temp AG,Switzerland","Research and Development team, Tool-Temp AG, Switzerland"],"affiliations":[{"raw_affiliation_string":"Research and Development team, Tool-Temp AG,Switzerland","institution_ids":["https://openalex.org/I136150977"]},{"raw_affiliation_string":"Research and Development team, Tool-Temp AG, Switzerland","institution_ids":["https://openalex.org/I136150977"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5069370342","display_name":"Armin Nurkanovi\u0107","orcid":"https://orcid.org/0000-0002-9796-4302"},"institutions":[{"id":"https://openalex.org/I161046081","display_name":"University of Freiburg","ror":"https://ror.org/0245cg223","country_code":"DE","type":"education","lineage":["https://openalex.org/I161046081"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Armin Nurkanovi\u0107","raw_affiliation_strings":["University of Freiburg,Department of Microsystems Engineering (IMTEK),Germany","Department of Microsystems Engineering (IMTEK), University of Freiburg, Germany"],"affiliations":[{"raw_affiliation_string":"University of Freiburg,Department of Microsystems Engineering (IMTEK),Germany","institution_ids":["https://openalex.org/I161046081"]},{"raw_affiliation_string":"Department of Microsystems Engineering (IMTEK), University of Freiburg, Germany","institution_ids":["https://openalex.org/I161046081"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5057375078","display_name":"Moritz Diehl","orcid":"https://orcid.org/0000-0001-6556-8252"},"institutions":[{"id":"https://openalex.org/I161046081","display_name":"University of Freiburg","ror":"https://ror.org/0245cg223","country_code":"DE","type":"education","lineage":["https://openalex.org/I161046081"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Moritz Diehl","raw_affiliation_strings":["University of Freiburg,Department of Microsystems Engineering (IMTEK) and Department of Mathematics,Germany","Department of Microsystems Engineering (IMTEK) and Department of Mathematics, University of Freiburg, Germany"],"affiliations":[{"raw_affiliation_string":"University of Freiburg,Department of Microsystems Engineering (IMTEK) and Department of Mathematics,Germany","institution_ids":["https://openalex.org/I161046081"]},{"raw_affiliation_string":"Department of Microsystems Engineering (IMTEK) and Department of Mathematics, University of Freiburg, Germany","institution_ids":["https://openalex.org/I161046081"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5081175634"],"corresponding_institution_ids":["https://openalex.org/I136150977"],"apc_list":null,"apc_paid":null,"fwci":0.4119,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.54273944,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":null,"issue":null,"first_page":"1","last_page":"7"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11416","display_name":"Numerical methods for differential equations","score":0.9998000264167786,"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":0.9998000264167786,"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/T10791","display_name":"Advanced Control Systems Optimization","score":0.9994999766349792,"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/T10173","display_name":"Computational Fluid Dynamics and Aerodynamics","score":0.9984999895095825,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"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/ode","display_name":"Ode","score":0.9705610275268555},{"id":"https://openalex.org/keywords/collocation","display_name":"Collocation (remote sensing)","score":0.7883816957473755},{"id":"https://openalex.org/keywords/ordinary-differential-equation","display_name":"Ordinary differential equation","score":0.7529401779174805},{"id":"https://openalex.org/keywords/optimal-control","display_name":"Optimal control","score":0.6390847563743591},{"id":"https://openalex.org/keywords/collocation-method","display_name":"Collocation method","score":0.5629638433456421},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5293049812316895},{"id":"https://openalex.org/keywords/state","display_name":"State (computer science)","score":0.5043848752975464},{"id":"https://openalex.org/keywords/orthogonal-collocation","display_name":"Orthogonal collocation","score":0.4555283188819885},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.4483111500740051},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4476024806499481},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.42718178033828735},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.413387656211853},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.3383181095123291},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.21233007311820984},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.18485099077224731}],"concepts":[{"id":"https://openalex.org/C34862557","wikidata":"https://www.wikidata.org/wiki/Q178985","display_name":"Ode","level":2,"score":0.9705610275268555},{"id":"https://openalex.org/C80023036","wikidata":"https://www.wikidata.org/wiki/Q5147531","display_name":"Collocation (remote sensing)","level":2,"score":0.7883816957473755},{"id":"https://openalex.org/C51544822","wikidata":"https://www.wikidata.org/wiki/Q465274","display_name":"Ordinary differential equation","level":3,"score":0.7529401779174805},{"id":"https://openalex.org/C91575142","wikidata":"https://www.wikidata.org/wiki/Q1971426","display_name":"Optimal control","level":2,"score":0.6390847563743591},{"id":"https://openalex.org/C2126413","wikidata":"https://www.wikidata.org/wiki/Q1779479","display_name":"Collocation method","level":4,"score":0.5629638433456421},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5293049812316895},{"id":"https://openalex.org/C48103436","wikidata":"https://www.wikidata.org/wiki/Q599031","display_name":"State (computer science)","level":2,"score":0.5043848752975464},{"id":"https://openalex.org/C114609681","wikidata":"https://www.wikidata.org/wiki/Q24839227","display_name":"Orthogonal collocation","level":5,"score":0.4555283188819885},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.4483111500740051},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4476024806499481},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.42718178033828735},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.413387656211853},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.3383181095123291},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.21233007311820984},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.18485099077224731},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.0},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.23919/ecc57647.2023.10178181","is_oa":false,"landing_page_url":"http://dx.doi.org/10.23919/ecc57647.2023.10178181","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2023 European Control Conference (ECC)","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Peace, Justice and strong institutions","score":0.8100000023841858,"id":"https://metadata.un.org/sdg/16"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":12,"referenced_works":["https://openalex.org/W648378158","https://openalex.org/W1972279567","https://openalex.org/W2054317073","https://openalex.org/W2071225300","https://openalex.org/W2090600907","https://openalex.org/W2123871098","https://openalex.org/W2788030459","https://openalex.org/W2842089854","https://openalex.org/W2945051793","https://openalex.org/W4255611696","https://openalex.org/W4283788456","https://openalex.org/W6762573877"],"related_works":["https://openalex.org/W2791210196","https://openalex.org/W2078318892","https://openalex.org/W4255016916","https://openalex.org/W2111003632","https://openalex.org/W2889856026","https://openalex.org/W1987365920","https://openalex.org/W1989122168","https://openalex.org/W2160114043","https://openalex.org/W2000247808","https://openalex.org/W2384941625"],"abstract_inverted_index":{"Mechanical":[0],"systems":[1],"are":[2],"usually":[3],"modeled":[4],"by":[5],"second-order":[6,87,129],"Ordinary":[7],"Differential":[8],"Equations":[9],"(ODE)":[10],"which":[11,68],"take":[12],"the":[13,38,48,51,61,71,74,93,109,116,132],"form":[14,135],"$\\ddot{q}=f(t,\\":[15,136],"q,\\":[16],"\\dot{q})$.":[17],"While":[18],"simulation":[19],"methods":[20,34],"tailored":[21,85,110],"to":[22,42,50,86,114],"these":[23],"equations":[24],"have":[25],"been":[26],"studied,":[27],"using":[28],"them":[29],"in":[30,101],"direct":[31,120],"optimal":[32,125],"control":[33,126],"is":[35,41,59,66,112],"rare.":[36],"Indeed,":[37],"standard":[39,94],"approach":[40,58,84],"perform":[43],"a":[44,102,119],"state":[45],"augmentation,":[46],"adding":[47],"velocities":[49],"state.":[52],"The":[53],"main":[54],"drawback":[55],"of":[56,63,73,118,131],"this":[57,79],"that":[60,108],"number":[62],"decision":[64],"variables":[65],"doubled,":[67],"could":[69],"harm":[70],"performance":[72,117],"resulting":[75],"optimization":[76],"problem.":[77],"In":[78],"paper,":[80],"we":[81,106],"present":[82],"an":[83],"ODE.":[88],"We":[89],"compare":[90],"it":[91],"with":[92,128],"one,":[95],"both":[96],"on":[97],"theoretical":[98],"aspects":[99],"and":[100],"numerical":[103],"example.":[104],"Notably,":[105],"show":[107],"formulation":[111],"likely":[113],"improve":[115],"collocation":[121],"method,":[122],"for":[123],"solving":[124],"problems":[127],"ODE":[130],"more":[133],"restrictive":[134],"q)$.":[137]},"counts_by_year":[{"year":2024,"cited_by_count":1}],"updated_date":"2025-12-19T19:40:27.379048","created_date":"2025-10-10T00:00:00"}
