{"id":"https://openalex.org/W2131875166","doi":"https://doi.org/10.1109/ecc.2015.7330694","title":"Parallel collocation solution of constrained optimal control problems","display_name":"Parallel collocation solution of constrained optimal control problems","publication_year":2015,"publication_date":"2015-07-01","ids":{"openalex":"https://openalex.org/W2131875166","doi":"https://doi.org/10.1109/ecc.2015.7330694","mag":"2131875166"},"language":"en","primary_location":{"id":"doi:10.1109/ecc.2015.7330694","is_oa":false,"landing_page_url":"https://doi.org/10.1109/ecc.2015.7330694","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2015 European Control Conference (ECC)","raw_type":"proceedings-article"},"type":"conference-paper","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/A5044727714","display_name":"Brian C. Fabien","orcid":"https://orcid.org/0000-0002-0663-021X"},"institutions":[{"id":"https://openalex.org/I201448701","display_name":"University of Washington","ror":"https://ror.org/00cvxb145","country_code":"US","type":"education","lineage":["https://openalex.org/I201448701"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Brian C. Fabien","raw_affiliation_strings":["Department of Mechanical Engineering, University of Washington, Seattle, WA, USA","Department of Mechanical Engineering, University of Washington, Seattle 98195, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mechanical Engineering, University of Washington, Seattle, WA, USA","institution_ids":["https://openalex.org/I201448701"]},{"raw_affiliation_string":"Department of Mechanical Engineering, University of Washington, Seattle 98195, USA","institution_ids":["https://openalex.org/I201448701"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5044727714"],"corresponding_institution_ids":["https://openalex.org/I201448701"],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":"1147","last_page":"1152"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11416","display_name":"Numerical methods for differential equations","score":0.9997000098228455,"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":0.9997000098228455,"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/T10173","display_name":"Computational Fluid Dynamics and Aerodynamics","score":0.9929999709129333,"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"}},{"id":"https://openalex.org/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.9839000105857849,"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/mathematics","display_name":"Mathematics","score":0.6368499398231506},{"id":"https://openalex.org/keywords/piecewise","display_name":"Piecewise","score":0.6025851368904114},{"id":"https://openalex.org/keywords/collocation-method","display_name":"Collocation method","score":0.5787453651428223},{"id":"https://openalex.org/keywords/jacobian-matrix-and-determinant","display_name":"Jacobian matrix and determinant","score":0.5712946057319641},{"id":"https://openalex.org/keywords/collocation","display_name":"Collocation (remote sensing)","score":0.5574696063995361},{"id":"https://openalex.org/keywords/algebraic-equation","display_name":"Algebraic equation","score":0.5450059771537781},{"id":"https://openalex.org/keywords/orthogonal-collocation","display_name":"Orthogonal collocation","score":0.5360085964202881},{"id":"https://openalex.org/keywords/boundary-value-problem","display_name":"Boundary value problem","score":0.49709466099739075},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.46515971422195435},{"id":"https://openalex.org/keywords/differential-algebraic-equation","display_name":"Differential algebraic equation","score":0.4621689021587372},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.37259507179260254},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.3067413568496704},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.2790294885635376},{"id":"https://openalex.org/keywords/ordinary-differential-equation","display_name":"Ordinary differential equation","score":0.26542505621910095},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.24223467707633972},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.18477869033813477}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6368499398231506},{"id":"https://openalex.org/C164660894","wikidata":"https://www.wikidata.org/wiki/Q2037833","display_name":"Piecewise","level":2,"score":0.6025851368904114},{"id":"https://openalex.org/C2126413","wikidata":"https://www.wikidata.org/wiki/Q1779479","display_name":"Collocation method","level":4,"score":0.5787453651428223},{"id":"https://openalex.org/C200331156","wikidata":"https://www.wikidata.org/wiki/Q506041","display_name":"Jacobian matrix and determinant","level":2,"score":0.5712946057319641},{"id":"https://openalex.org/C80023036","wikidata":"https://www.wikidata.org/wiki/Q5147531","display_name":"Collocation (remote sensing)","level":2,"score":0.5574696063995361},{"id":"https://openalex.org/C23917780","wikidata":"https://www.wikidata.org/wiki/Q50698","display_name":"Algebraic equation","level":3,"score":0.5450059771537781},{"id":"https://openalex.org/C114609681","wikidata":"https://www.wikidata.org/wiki/Q24839227","display_name":"Orthogonal collocation","level":5,"score":0.5360085964202881},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.49709466099739075},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.46515971422195435},{"id":"https://openalex.org/C186219872","wikidata":"https://www.wikidata.org/wiki/Q955889","display_name":"Differential algebraic equation","level":4,"score":0.4621689021587372},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.37259507179260254},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.3067413568496704},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2790294885635376},{"id":"https://openalex.org/C51544822","wikidata":"https://www.wikidata.org/wiki/Q465274","display_name":"Ordinary differential equation","level":3,"score":0.26542505621910095},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.24223467707633972},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.18477869033813477},{"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/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/ecc.2015.7330694","is_oa":false,"landing_page_url":"https://doi.org/10.1109/ecc.2015.7330694","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2015 European Control Conference (ECC)","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/10","display_name":"Reduced inequalities","score":0.5099999904632568}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":18,"referenced_works":["https://openalex.org/W9124626","https://openalex.org/W1509923322","https://openalex.org/W1520090149","https://openalex.org/W1971661442","https://openalex.org/W1981338751","https://openalex.org/W1982019931","https://openalex.org/W1988974867","https://openalex.org/W1995504856","https://openalex.org/W2006743728","https://openalex.org/W2030049571","https://openalex.org/W2042388195","https://openalex.org/W2049533325","https://openalex.org/W2059586616","https://openalex.org/W2069809965","https://openalex.org/W2083431695","https://openalex.org/W2145800024","https://openalex.org/W2312216956","https://openalex.org/W3209416867"],"related_works":["https://openalex.org/W2791210196","https://openalex.org/W2078318892","https://openalex.org/W4255016916","https://openalex.org/W2111003632","https://openalex.org/W1987365920","https://openalex.org/W2889856026","https://openalex.org/W1989122168","https://openalex.org/W2150070385","https://openalex.org/W2000247808","https://openalex.org/W2384941625"],"abstract_inverted_index":{"This":[0],"paper":[1],"presents":[2],"a":[3,11,71,118,145,155],"parallel":[4,102,108,115,137],"collocation":[5,53,87,106],"algorithm":[6,100],"for":[7],"the":[8,36,40,52,57,63,86,93,99,105,111,127,136,149],"solution":[9,41,116],"of":[10,31,42,62,92,98,104,110,117,148],"two-point":[12],"boundary":[13],"value":[14],"problem":[15],"(BVP)":[16],"that":[17,46,73,135],"involves":[18,101],"index-1":[19],"differential-algebraic":[20],"equations":[21],"(DAEs)":[22],"and":[23,59,89,114,151],"inequality":[24,49,94],"constraints":[25],"due":[26],"to":[27,39,84,125,144,154],"complementarity":[28],"conditions.":[29],"BVP-DAEs":[30,64],"this":[32],"type":[33],"arise":[34],"from":[35],"indirect":[37],"approach":[38],"optimal":[43],"control":[44,47],"problems":[45],"variable":[48],"constraints.":[50,95],"In":[51],"method":[54,81],"presented":[55],"here":[56],"differential":[58],"algebraic":[60],"variables":[61],"are":[65],"approximated":[66],"using":[67],"piecewise":[68],"polynomials":[69],"on":[70],"mesh":[72],"may":[74],"be":[75],"nonuniform.":[76],"A":[77,131],"Newton":[78,128],"interior":[79],"point":[80],"is":[82],"used":[83],"solve":[85],"equations,":[88,107],"maintain":[90],"feasibility":[91],"The":[96],"implementation":[97,138],"evaluation":[103,109],"system":[112,124],"Jacobian,":[113],"boarded":[119],"almost":[120],"block":[121],"diagonal":[122],"(BABD)":[123],"obtain":[126],"search":[129],"direction.":[130],"numerical":[132],"example":[133],"shows":[134],"provides":[139],"significant":[140],"speedup":[141],"when":[142,152],"compared":[143,153],"sequential":[146],"version":[147],"algorithm,":[150],"direct":[156],"method.":[157]},"counts_by_year":[{"year":2016,"cited_by_count":1}],"updated_date":"2026-07-14T23:27:15.235271","created_date":"2025-10-10T00:00:00"}