{"id":"https://openalex.org/W2494394972","doi":"https://doi.org/10.1109/acc.2016.7524918","title":"Convergence rates for direct transcription of optimal control problems using Second Derivative Methods","display_name":"Convergence rates for direct transcription of optimal control problems using Second Derivative Methods","publication_year":2016,"publication_date":"2016-07-01","ids":{"openalex":"https://openalex.org/W2494394972","doi":"https://doi.org/10.1109/acc.2016.7524918","mag":"2494394972"},"language":"en","primary_location":{"id":"doi:10.1109/acc.2016.7524918","is_oa":false,"landing_page_url":"https://doi.org/10.1109/acc.2016.7524918","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2016 American Control Conference (ACC)","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/A5058282306","display_name":"Dayaram Sonawane","orcid":"https://orcid.org/0000-0002-4298-9879"},"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":"Dayaram Sonawane","raw_affiliation_strings":["Department of Chemical Engineering, University of Washington, Seattle, WA, USA"],"affiliations":[{"raw_affiliation_string":"Department of Chemical Engineering, University of Washington, Seattle, WA, USA","institution_ids":["https://openalex.org/I201448701"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5052135459","display_name":"Manan Pathak","orcid":"https://orcid.org/0000-0003-2069-9288"},"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":false,"raw_author_name":"Manan Pathak","raw_affiliation_strings":["Department of Chemical Engineering, University of Washington, Seattle, WA, USA"],"affiliations":[{"raw_affiliation_string":"Department of Chemical Engineering, University of Washington, Seattle, WA, USA","institution_ids":["https://openalex.org/I201448701"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5046553570","display_name":"Venkat R. Subramanian","orcid":"https://orcid.org/0000-0002-2092-9744"},"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"]},{"id":"https://openalex.org/I142606810","display_name":"Pacific Northwest National Laboratory","ror":"https://ror.org/05h992307","country_code":"US","type":"facility","lineage":["https://openalex.org/I1325736334","https://openalex.org/I1330989302","https://openalex.org/I142606810","https://openalex.org/I39565521"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Venkat R. Subramanian","raw_affiliation_strings":["Department of Chemical Engineering, University of Washington, Seattle, WA, USA","The Pacific Northwest National Laboratory (PNNL), Richland, WA, USA"],"affiliations":[{"raw_affiliation_string":"Department of Chemical Engineering, University of Washington, Seattle, WA, USA","institution_ids":["https://openalex.org/I201448701"]},{"raw_affiliation_string":"The Pacific Northwest National Laboratory (PNNL), Richland, WA, USA","institution_ids":["https://openalex.org/I142606810"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5058282306"],"corresponding_institution_ids":["https://openalex.org/I201448701"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.0923923,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":"215","last_page":"220"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11416","display_name":"Numerical methods for differential equations","score":0.9991999864578247,"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":0.9991999864578247,"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/T11082","display_name":"Spacecraft Dynamics and Control","score":0.9988999962806702,"subfield":{"id":"https://openalex.org/subfields/2202","display_name":"Aerospace 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/T10792","display_name":"Matrix Theory and Algorithms","score":0.9966999888420105,"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/discretization","display_name":"Discretization","score":0.8686816692352295},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.764603853225708},{"id":"https://openalex.org/keywords/optimal-control","display_name":"Optimal control","score":0.6553909182548523},{"id":"https://openalex.org/keywords/rate-of-convergence","display_name":"Rate of convergence","score":0.5875918865203857},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.534468948841095},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.46029719710350037},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.46025550365448},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.438963919878006},{"id":"https://openalex.org/keywords/derivative","display_name":"Derivative (finance)","score":0.4150657653808594},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.3928471803665161},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.34170758724212646},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.08964037895202637},{"id":"https://openalex.org/keywords/key","display_name":"Key (lock)","score":0.051724910736083984}],"concepts":[{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.8686816692352295},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.764603853225708},{"id":"https://openalex.org/C91575142","wikidata":"https://www.wikidata.org/wiki/Q1971426","display_name":"Optimal control","level":2,"score":0.6553909182548523},{"id":"https://openalex.org/C57869625","wikidata":"https://www.wikidata.org/wiki/Q1783502","display_name":"Rate of convergence","level":3,"score":0.5875918865203857},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.534468948841095},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.46029719710350037},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.46025550365448},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.438963919878006},{"id":"https://openalex.org/C111771559","wikidata":"https://www.wikidata.org/wiki/Q66295","display_name":"Derivative (finance)","level":2,"score":0.4150657653808594},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.3928471803665161},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.34170758724212646},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.08964037895202637},{"id":"https://openalex.org/C26517878","wikidata":"https://www.wikidata.org/wiki/Q228039","display_name":"Key (lock)","level":2,"score":0.051724910736083984},{"id":"https://openalex.org/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","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/C106159729","wikidata":"https://www.wikidata.org/wiki/Q2294553","display_name":"Financial economics","level":1,"score":0.0},{"id":"https://openalex.org/C38652104","wikidata":"https://www.wikidata.org/wiki/Q3510521","display_name":"Computer security","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}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/acc.2016.7524918","is_oa":false,"landing_page_url":"https://doi.org/10.1109/acc.2016.7524918","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2016 American Control Conference (ACC)","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320306854","display_name":"Washington Research Foundation","ror":"https://ror.org/00hasdx88"},{"id":"https://openalex.org/F4320332276","display_name":"Advanced Research Projects Agency - Energy","ror":"https://ror.org/03q1rgc19"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":26,"referenced_works":["https://openalex.org/W1509923322","https://openalex.org/W1587799944","https://openalex.org/W1987694238","https://openalex.org/W1995504856","https://openalex.org/W2018816843","https://openalex.org/W2027472105","https://openalex.org/W2029290244","https://openalex.org/W2031291057","https://openalex.org/W2035273811","https://openalex.org/W2041409372","https://openalex.org/W2057998877","https://openalex.org/W2070630896","https://openalex.org/W2072235453","https://openalex.org/W2080526106","https://openalex.org/W2082764901","https://openalex.org/W2101336970","https://openalex.org/W2107345353","https://openalex.org/W2133413084","https://openalex.org/W2140377302","https://openalex.org/W2158128919","https://openalex.org/W2159294788","https://openalex.org/W2162218551","https://openalex.org/W2333858667","https://openalex.org/W2334591577","https://openalex.org/W3102507213","https://openalex.org/W4301649152"],"related_works":["https://openalex.org/W2006251942","https://openalex.org/W2364741597","https://openalex.org/W1492103595","https://openalex.org/W1864774435","https://openalex.org/W946352265","https://openalex.org/W3020787026","https://openalex.org/W2334479858","https://openalex.org/W2799209613","https://openalex.org/W2793786119","https://openalex.org/W1507702947"],"abstract_inverted_index":{"In":[0],"this":[1],"paper,":[2],"Second":[3],"Derivative":[4],"Method":[5],"(SDM)":[6],"of":[7,25,32,48,52,56,83,110,121],"numerical":[8],"discretization":[9],"is":[10,71,98,128],"applied":[11],"to":[12,42,130,133],"optimal":[13,33,77],"control":[14,34,78],"problems.":[15],"Convergence":[16],"rates":[17,55],"for":[18,76,90,96,101,137],"the":[19,22,28,44,53,86,119,125],"error":[20],"between":[21],"discretized":[23],"solution":[24,31],"SDM":[26,57],"and":[27,46,66,92,136],"corresponding":[29],"analytical":[30],"problems":[35,79],"are":[36,40],"analyzed.":[37],"Illustrative":[38],"examples":[39],"included":[41],"demonstrate":[43],"applicability":[45],"benefits":[47],"SDM.":[49],"The":[50],"comparison":[51],"convergence":[54,89,95,111],"with":[58,80],"implicit":[59],"Runge-Kutta":[60],"methods":[61],"(third":[62],"order,":[63,68],"2-stage":[64],"RadauIIA":[65],"fourth":[67,87],"3-stage":[69],"LobattoIIIA)":[70],"also":[72],"presented.":[73],"Using":[74],"SDM,":[75],"non-stiff":[81],"type":[82],"state":[84],"equations,":[85,104],"order":[88,94,109],"states":[91],"second":[93],"controls":[97],"observed,":[99],"while":[100],"certain":[102,138],"stiff/oscillatory":[103],"it":[105],"results":[106],"in":[107,114],"reduced":[108],"as":[112],"observed":[113],"other":[115,134],"approaches.":[116],"Depending":[117],"on":[118],"choice":[120],"optimization":[122],"algorithms/platforms":[123],"used,":[124],"proposed":[126],"method":[127],"found":[129],"be":[131],"comparable":[132],"approaches":[135],"cases,":[139],"more":[140],"efficient.":[141]},"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
