{"id":"https://openalex.org/W2127721063","doi":"https://doi.org/10.1109/acc.2006.1655348","title":"Convergence rates for direct transcription of optimal control problems with final-time equality constraints using collocation at Radau points","display_name":"Convergence rates for direct transcription of optimal control problems with final-time equality constraints using collocation at Radau points","publication_year":2006,"publication_date":"2006-01-01","ids":{"openalex":"https://openalex.org/W2127721063","doi":"https://doi.org/10.1109/acc.2006.1655348","mag":"2127721063"},"language":"en","primary_location":{"id":"doi:10.1109/acc.2006.1655348","is_oa":false,"landing_page_url":"https://doi.org/10.1109/acc.2006.1655348","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2006 American Control Conference","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/A5074451300","display_name":"S. Karneswaran","orcid":null},"institutions":[{"id":"https://openalex.org/I74973139","display_name":"Carnegie Mellon University","ror":"https://ror.org/05x2bcf33","country_code":"US","type":"education","lineage":["https://openalex.org/I74973139"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"S. Karneswaran","raw_affiliation_strings":["Carnegie Mellon University, Pittsburgh, PA, US","Dept. of Chem. Eng., Carnegie Mellon Univ., Pittsburgh, PA, USA#TAB#"],"affiliations":[{"raw_affiliation_string":"Carnegie Mellon University, Pittsburgh, PA, US","institution_ids":["https://openalex.org/I74973139"]},{"raw_affiliation_string":"Dept. of Chem. Eng., Carnegie Mellon Univ., Pittsburgh, PA, USA#TAB#","institution_ids":["https://openalex.org/I74973139"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5052825722","display_name":"Lorenz T. Biegler","orcid":"https://orcid.org/0000-0003-3875-4441"},"institutions":[{"id":"https://openalex.org/I74973139","display_name":"Carnegie Mellon University","ror":"https://ror.org/05x2bcf33","country_code":"US","type":"education","lineage":["https://openalex.org/I74973139"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"L.T. Biegler","raw_affiliation_strings":["Professor of Chemical Engineering, Carnegie Mellon University, Pittsburgh, PA, USA","Dept. of Chem. Eng., Carnegie Mellon Univ., Pittsburgh, PA, USA#TAB#"],"affiliations":[{"raw_affiliation_string":"Professor of Chemical Engineering, Carnegie Mellon University, Pittsburgh, PA, USA","institution_ids":["https://openalex.org/I74973139"]},{"raw_affiliation_string":"Dept. of Chem. Eng., Carnegie Mellon Univ., Pittsburgh, PA, USA#TAB#","institution_ids":["https://openalex.org/I74973139"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5074451300"],"corresponding_institution_ids":["https://openalex.org/I74973139"],"apc_list":null,"apc_paid":null,"fwci":2.0569,"has_fulltext":false,"cited_by_count":9,"citation_normalized_percentile":{"value":0.86680111,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11245","display_name":"Advanced Numerical Analysis Techniques","score":0.9994999766349792,"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"}},"topics":[{"id":"https://openalex.org/T11245","display_name":"Advanced Numerical Analysis Techniques","score":0.9994999766349792,"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":0.9984999895095825,"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"}},{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.9970999956130981,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/controllability","display_name":"Controllability","score":0.7839259505271912},{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.7509037852287292},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.6298328638076782},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.6079518795013428},{"id":"https://openalex.org/keywords/optimal-control","display_name":"Optimal control","score":0.6038902997970581},{"id":"https://openalex.org/keywords/collocation","display_name":"Collocation (remote sensing)","score":0.5639453530311584},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5101907253265381},{"id":"https://openalex.org/keywords/lagrange-multiplier","display_name":"Lagrange multiplier","score":0.44275957345962524},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4140446186065674},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.38150644302368164},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.08600345253944397}],"concepts":[{"id":"https://openalex.org/C48209547","wikidata":"https://www.wikidata.org/wiki/Q1331104","display_name":"Controllability","level":2,"score":0.7839259505271912},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.7509037852287292},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.6298328638076782},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.6079518795013428},{"id":"https://openalex.org/C91575142","wikidata":"https://www.wikidata.org/wiki/Q1971426","display_name":"Optimal control","level":2,"score":0.6038902997970581},{"id":"https://openalex.org/C80023036","wikidata":"https://www.wikidata.org/wiki/Q5147531","display_name":"Collocation (remote sensing)","level":2,"score":0.5639453530311584},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5101907253265381},{"id":"https://openalex.org/C73684929","wikidata":"https://www.wikidata.org/wiki/Q598870","display_name":"Lagrange multiplier","level":2,"score":0.44275957345962524},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4140446186065674},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.38150644302368164},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.08600345253944397},{"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/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/acc.2006.1655348","is_oa":false,"landing_page_url":"https://doi.org/10.1109/acc.2006.1655348","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2006 American Control Conference","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.46000000834465027,"display_name":"Peace, Justice and strong institutions","id":"https://metadata.un.org/sdg/16"},{"score":0.4300000071525574,"display_name":"Reduced inequalities","id":"https://metadata.un.org/sdg/10"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":12,"referenced_works":["https://openalex.org/W30339796","https://openalex.org/W1594348529","https://openalex.org/W1597944220","https://openalex.org/W1973942504","https://openalex.org/W1987541911","https://openalex.org/W1987694238","https://openalex.org/W2031291057","https://openalex.org/W2035273811","https://openalex.org/W2051373638","https://openalex.org/W2798500587","https://openalex.org/W3029645440","https://openalex.org/W4293775970"],"related_works":["https://openalex.org/W2036697162","https://openalex.org/W2332386680","https://openalex.org/W2561315646","https://openalex.org/W2248621902","https://openalex.org/W2003779889","https://openalex.org/W4205698120","https://openalex.org/W4239246781","https://openalex.org/W2542825942","https://openalex.org/W3201620972","https://openalex.org/W2022062253"],"abstract_inverted_index":{"In":[0],"this":[1],"paper,":[2],"we":[3,67],"present":[4],"convergence":[5,46,62],"rates":[6],"for":[7,78],"the":[8,11,16,32,56,61,75,79],"error":[9],"between":[10],"direct":[12],"transcription":[13],"solution":[14,18],"and":[15],"true":[17],"of":[19,31,58],"an":[20,48,65,69],"optimal":[21],"control":[22],"problem":[23,36],"with":[24],"final-time":[25],"equality":[26],"constraints,":[27],"as":[28],"a":[29],"function":[30],"discretization":[33],"size.":[34],"The":[35,52],"is":[37],"discretized":[38],"using":[39],"collocation":[40],"at":[41],"Radau":[42],"points.":[43],"We":[44],"analyze":[45],"from":[47,74],"NLP/matrix":[49],"algebra":[50],"perspective.":[51],"work":[53],"also":[54],"reveals":[55],"role":[57],"controllability":[59],"in":[60],"analysis.":[63],"As":[64],"outcome,":[66],"have":[68],"adjoint":[70],"estimation":[71],"procedure":[72],"derived":[73],"Lagrange":[76],"multipliers":[77],"large":[80],"scale":[81],"NLP":[82]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2013,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}