{"id":"https://openalex.org/W2047749334","doi":"https://doi.org/10.1007/s10589-007-9102-4","title":"Connections between the covector mapping theorem and convergence of pseudospectral methods for optimal control","display_name":"Connections between the covector mapping theorem and convergence of pseudospectral methods for optimal control","publication_year":2007,"publication_date":"2007-10-30","ids":{"openalex":"https://openalex.org/W2047749334","doi":"https://doi.org/10.1007/s10589-007-9102-4","mag":"2047749334"},"language":"en","primary_location":{"id":"doi:10.1007/s10589-007-9102-4","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10589-007-9102-4","pdf_url":null,"source":{"id":"https://openalex.org/S39243548","display_name":"Computational Optimization and Applications","issn_l":"0926-6003","issn":["0926-6003","1573-2894"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computational Optimization and Applications","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://escholarship.org/content/qt3rr9k9mf/qt3rr9k9mf.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5069454917","display_name":"Qi Gong","orcid":"https://orcid.org/0000-0003-0398-5792"},"institutions":[{"id":"https://openalex.org/I45438204","display_name":"The University of Texas at San Antonio","ror":"https://ror.org/01kd65564","country_code":"US","type":"education","lineage":["https://openalex.org/I45438204"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Qi Gong","raw_affiliation_strings":["Department of Electrical & Computer Engineering, University of Texas at San Antonio, San Antonio, TX, 78249-1644, USA","Department of Electrical & Computer Engineering, University of Texas at San Antonio, San Antonio, USA 78249-1644#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Electrical & Computer Engineering, University of Texas at San Antonio, San Antonio, TX, 78249-1644, USA","institution_ids":["https://openalex.org/I45438204"]},{"raw_affiliation_string":"Department of Electrical & Computer Engineering, University of Texas at San Antonio, San Antonio, USA 78249-1644#TAB#","institution_ids":["https://openalex.org/I45438204"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5057121880","display_name":"I. Michael Ross","orcid":null},"institutions":[{"id":"https://openalex.org/I35364215","display_name":"Naval Postgraduate School","ror":"https://ror.org/033yfkj90","country_code":"US","type":"education","lineage":["https://openalex.org/I1330347796","https://openalex.org/I3130687028","https://openalex.org/I35364215"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"I. Michael Ross","raw_affiliation_strings":["Department of Mechanical and Astronautical Engineering, Naval Postgraduate School, Monterey, CA, 93943, USA","Department of Mechanical and Astronautical Engineering, Naval Postgraduate School, Monterey, USA 93943#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mechanical and Astronautical Engineering, Naval Postgraduate School, Monterey, CA, 93943, USA","institution_ids":["https://openalex.org/I35364215"]},{"raw_affiliation_string":"Department of Mechanical and Astronautical Engineering, Naval Postgraduate School, Monterey, USA 93943#TAB#","institution_ids":["https://openalex.org/I35364215"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100751181","display_name":"Wei Kang","orcid":"https://orcid.org/0000-0002-1194-722X"},"institutions":[{"id":"https://openalex.org/I35364215","display_name":"Naval Postgraduate School","ror":"https://ror.org/033yfkj90","country_code":"US","type":"education","lineage":["https://openalex.org/I1330347796","https://openalex.org/I3130687028","https://openalex.org/I35364215"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Wei Kang","raw_affiliation_strings":["Department of Applied Mathematics, Naval Postgraduate School, Monterey, CA, 93943, USA","Department of Applied Mathematics, Naval Postgraduate School, Monterey, USA 93943#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics, Naval Postgraduate School, Monterey, CA, 93943, USA","institution_ids":["https://openalex.org/I35364215"]},{"raw_affiliation_string":"Department of Applied Mathematics, Naval Postgraduate School, Monterey, USA 93943#TAB#","institution_ids":["https://openalex.org/I35364215"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5110239250","display_name":"Fariba Fahroo","orcid":null},"institutions":[{"id":"https://openalex.org/I35364215","display_name":"Naval Postgraduate School","ror":"https://ror.org/033yfkj90","country_code":"US","type":"education","lineage":["https://openalex.org/I1330347796","https://openalex.org/I3130687028","https://openalex.org/I35364215"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Fariba Fahroo","raw_affiliation_strings":["Department of Applied Mathematics, Naval Postgraduate School, Monterey, CA, 93943, USA","Department of Applied Mathematics, Naval Postgraduate School, Monterey, USA 93943#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics, Naval Postgraduate School, Monterey, CA, 93943, USA","institution_ids":["https://openalex.org/I35364215"]},{"raw_affiliation_string":"Department of Applied Mathematics, Naval Postgraduate School, Monterey, USA 93943#TAB#","institution_ids":["https://openalex.org/I35364215"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5069454917"],"corresponding_institution_ids":["https://openalex.org/I45438204"],"apc_list":{"value":2390,"currency":"EUR","value_usd":2990},"apc_paid":null,"fwci":340.4014,"has_fulltext":true,"cited_by_count":185,"citation_normalized_percentile":{"value":0.99977834,"is_in_top_1_percent":true,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":94,"max":100},"biblio":{"volume":"41","issue":"3","first_page":"307","last_page":"335"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11082","display_name":"Spacecraft Dynamics and Control","score":0.9998999834060669,"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"}},"topics":[{"id":"https://openalex.org/T11082","display_name":"Spacecraft Dynamics and Control","score":0.9998999834060669,"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/T13855","display_name":"Aerospace Engineering and Control Systems","score":0.9955999851226807,"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/T11325","display_name":"Inertial Sensor and Navigation","score":0.9872000217437744,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7840932607650757},{"id":"https://openalex.org/keywords/optimal-control","display_name":"Optimal control","score":0.7481575608253479},{"id":"https://openalex.org/keywords/gauss-pseudospectral-method","display_name":"Gauss pseudospectral method","score":0.7002097964286804},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.6780734062194824},{"id":"https://openalex.org/keywords/dual-polyhedron","display_name":"Dual polyhedron","score":0.5603999495506287},{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.5591654777526855},{"id":"https://openalex.org/keywords/pseudospectral-optimal-control","display_name":"Pseudospectral optimal control","score":0.5241879820823669},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.49612411856651306},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.495585560798645},{"id":"https://openalex.org/keywords/modes-of-convergence","display_name":"Modes of convergence (annotated index)","score":0.49339261651039124},{"id":"https://openalex.org/keywords/compact-convergence","display_name":"Compact convergence","score":0.472265362739563},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.45078766345977783},{"id":"https://openalex.org/keywords/control-variable","display_name":"Control variable","score":0.4393536150455475},{"id":"https://openalex.org/keywords/pseudo-spectral-method","display_name":"Pseudo-spectral method","score":0.24086526036262512},{"id":"https://openalex.org/keywords/rate-of-convergence","display_name":"Rate of convergence","score":0.22099635004997253},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.15316367149353027},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.15256312489509583},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.09617474675178528}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7840932607650757},{"id":"https://openalex.org/C91575142","wikidata":"https://www.wikidata.org/wiki/Q1971426","display_name":"Optimal control","level":2,"score":0.7481575608253479},{"id":"https://openalex.org/C71026131","wikidata":"https://www.wikidata.org/wiki/Q5527825","display_name":"Gauss pseudospectral method","level":5,"score":0.7002097964286804},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.6780734062194824},{"id":"https://openalex.org/C105313907","wikidata":"https://www.wikidata.org/wiki/Q1053857","display_name":"Dual polyhedron","level":2,"score":0.5603999495506287},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.5591654777526855},{"id":"https://openalex.org/C154304650","wikidata":"https://www.wikidata.org/wiki/Q7255577","display_name":"Pseudospectral optimal control","level":5,"score":0.5241879820823669},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.49612411856651306},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.495585560798645},{"id":"https://openalex.org/C48216909","wikidata":"https://www.wikidata.org/wiki/Q6889156","display_name":"Modes of convergence (annotated index)","level":5,"score":0.49339261651039124},{"id":"https://openalex.org/C5871375","wikidata":"https://www.wikidata.org/wiki/Q1780715","display_name":"Compact convergence","level":4,"score":0.472265362739563},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.45078766345977783},{"id":"https://openalex.org/C153240184","wikidata":"https://www.wikidata.org/wiki/Q3243772","display_name":"Control variable","level":2,"score":0.4393536150455475},{"id":"https://openalex.org/C177937620","wikidata":"https://www.wikidata.org/wiki/Q7254447","display_name":"Pseudo-spectral method","level":4,"score":0.24086526036262512},{"id":"https://openalex.org/C57869625","wikidata":"https://www.wikidata.org/wiki/Q1783502","display_name":"Rate of convergence","level":3,"score":0.22099635004997253},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.15316367149353027},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.15256312489509583},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.09617474675178528},{"id":"https://openalex.org/C127162648","wikidata":"https://www.wikidata.org/wiki/Q16858953","display_name":"Channel (broadcasting)","level":2,"score":0.0},{"id":"https://openalex.org/C203024314","wikidata":"https://www.wikidata.org/wiki/Q1365258","display_name":"Fourier analysis","level":3,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C47776270","wikidata":"https://www.wikidata.org/wiki/Q1455249","display_name":"Topological vector space","level":3,"score":0.0},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0},{"id":"https://openalex.org/C81332173","wikidata":"https://www.wikidata.org/wiki/Q179899","display_name":"Topological space","level":2,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C102519508","wikidata":"https://www.wikidata.org/wiki/Q6520159","display_name":"Fourier transform","level":2,"score":0.0},{"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/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"score":0.0},{"id":"https://openalex.org/C174265945","wikidata":"https://www.wikidata.org/wiki/Q1142889","display_name":"Isolated point","level":4,"score":0.0},{"id":"https://openalex.org/C31258907","wikidata":"https://www.wikidata.org/wiki/Q1301371","display_name":"Computer network","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1007/s10589-007-9102-4","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10589-007-9102-4","pdf_url":null,"source":{"id":"https://openalex.org/S39243548","display_name":"Computational Optimization and Applications","issn_l":"0926-6003","issn":["0926-6003","1573-2894"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computational Optimization and Applications","raw_type":"journal-article"},{"id":"pmh:qt3rr9k9mf","is_oa":true,"landing_page_url":"http://www.escholarship.org/uc/item/3rr9k9mf","pdf_url":"https://escholarship.org/content/qt3rr9k9mf/qt3rr9k9mf.pdf","source":{"id":"https://openalex.org/S4306400115","display_name":"eScholarship (California Digital Library)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I2801248553","host_organization_name":"California Digital Library","host_organization_lineage":["https://openalex.org/I2801248553"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Gong, Q; Ross, IM; Kang, W; &amp; Fahroo, F. (2007). Connections between the covector mapping theorem and convergence of pseudospectral methods for optimal control. Computational Optimization and Applications, 41(3), 307 - 335. doi: 10.1007/s10589-007-9102-4. UC Santa Cruz: Retrieved from: http://www.escholarship.org/uc/item/3rr9k9mf","raw_type":"article"},{"id":"pmh:oai:calhoun.nps.edu:10945/48182","is_oa":false,"landing_page_url":"http://hdl.handle.net/10945/48182","pdf_url":null,"source":{"id":"https://openalex.org/S4306400952","display_name":"Calhoun: The Naval Postgraduate School Institutional Archive (Naval Postgraduate School)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I35364215","host_organization_name":"Naval Postgraduate School","host_organization_lineage":["https://openalex.org/I35364215"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Article"},{"id":"pmh:oai:escholarship.org/ark:/13030/qt3rr9k9mf","is_oa":false,"landing_page_url":"https://escholarship.org/uc/item/3rr9k9mf","pdf_url":null,"source":{"id":"https://openalex.org/S4306400115","display_name":"eScholarship (California Digital Library)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I2801248553","host_organization_name":"California Digital Library","host_organization_lineage":["https://openalex.org/I2801248553"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Computational Optimization and Applications, vol 41, iss 3","raw_type":"article"}],"best_oa_location":{"id":"pmh:qt3rr9k9mf","is_oa":true,"landing_page_url":"http://www.escholarship.org/uc/item/3rr9k9mf","pdf_url":"https://escholarship.org/content/qt3rr9k9mf/qt3rr9k9mf.pdf","source":{"id":"https://openalex.org/S4306400115","display_name":"eScholarship (California Digital Library)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I2801248553","host_organization_name":"California Digital Library","host_organization_lineage":["https://openalex.org/I2801248553"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Gong, Q; Ross, IM; Kang, W; &amp; Fahroo, F. (2007). Connections between the covector mapping theorem and convergence of pseudospectral methods for optimal control. Computational Optimization and Applications, 41(3), 307 - 335. doi: 10.1007/s10589-007-9102-4. UC Santa Cruz: Retrieved from: http://www.escholarship.org/uc/item/3rr9k9mf","raw_type":"article"},"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320338279","display_name":"Air Force Office of Scientific Research","ror":"https://ror.org/011e9bt93"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2047749334.pdf","grobid_xml":"https://content.openalex.org/works/W2047749334.grobid-xml"},"referenced_works_count":58,"referenced_works":["https://openalex.org/W113966369","https://openalex.org/W176320170","https://openalex.org/W414266413","https://openalex.org/W641945295","https://openalex.org/W822748439","https://openalex.org/W1490180844","https://openalex.org/W1537335979","https://openalex.org/W1577968762","https://openalex.org/W1587799944","https://openalex.org/W1588578418","https://openalex.org/W1623487976","https://openalex.org/W1805381866","https://openalex.org/W1976616156","https://openalex.org/W1982019931","https://openalex.org/W1985249384","https://openalex.org/W2000639728","https://openalex.org/W2003281007","https://openalex.org/W2005205022","https://openalex.org/W2011302318","https://openalex.org/W2018816843","https://openalex.org/W2022144657","https://openalex.org/W2027181737","https://openalex.org/W2031291057","https://openalex.org/W2032506563","https://openalex.org/W2034877161","https://openalex.org/W2052551315","https://openalex.org/W2067820110","https://openalex.org/W2080132051","https://openalex.org/W2085015797","https://openalex.org/W2085609242","https://openalex.org/W2102884619","https://openalex.org/W2119664948","https://openalex.org/W2134298283","https://openalex.org/W2137413756","https://openalex.org/W2145603256","https://openalex.org/W2153425320","https://openalex.org/W2167761964","https://openalex.org/W2171920051","https://openalex.org/W2187565700","https://openalex.org/W2318766709","https://openalex.org/W2320670471","https://openalex.org/W2335113348","https://openalex.org/W2566565178","https://openalex.org/W2798500587","https://openalex.org/W2798574506","https://openalex.org/W2798737326","https://openalex.org/W3020818366","https://openalex.org/W3029645440","https://openalex.org/W3040464464","https://openalex.org/W3133127499","https://openalex.org/W3157341860","https://openalex.org/W3206777520","https://openalex.org/W4236400251","https://openalex.org/W4246616525","https://openalex.org/W4285719527","https://openalex.org/W4293775970","https://openalex.org/W4296154082","https://openalex.org/W4298060601"],"related_works":["https://openalex.org/W2141789111","https://openalex.org/W2089701552","https://openalex.org/W2070392617","https://openalex.org/W2392310195","https://openalex.org/W3095545966","https://openalex.org/W3084136071","https://openalex.org/W2377150087","https://openalex.org/W2212154411","https://openalex.org/W4308701511","https://openalex.org/W2047749334"],"abstract_inverted_index":null,"counts_by_year":[{"year":2025,"cited_by_count":5},{"year":2024,"cited_by_count":7},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":6},{"year":2021,"cited_by_count":8},{"year":2020,"cited_by_count":10},{"year":2019,"cited_by_count":10},{"year":2018,"cited_by_count":13},{"year":2017,"cited_by_count":7},{"year":2016,"cited_by_count":22},{"year":2015,"cited_by_count":10},{"year":2014,"cited_by_count":17},{"year":2013,"cited_by_count":11},{"year":2012,"cited_by_count":11}],"updated_date":"2026-06-19T15:47:20.252518","created_date":"2025-10-10T00:00:00"}
