{"id":"https://openalex.org/W3162910870","doi":"https://doi.org/10.1109/tac.2021.3079185","title":"A Successive Pseudospectral-Based Approximation of the Solution of Regulator Equations","display_name":"A Successive Pseudospectral-Based Approximation of the Solution of Regulator Equations","publication_year":2021,"publication_date":"2021-05-11","ids":{"openalex":"https://openalex.org/W3162910870","doi":"https://doi.org/10.1109/tac.2021.3079185","mag":"3162910870"},"language":"en","primary_location":{"id":"doi:10.1109/tac.2021.3079185","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tac.2021.3079185","pdf_url":null,"source":{"id":"https://openalex.org/S184954342","display_name":"IEEE Transactions on Automatic Control","issn_l":"0018-9286","issn":["0018-9286","1558-2523","2334-3303"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Automatic Control","raw_type":"journal-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/A5051158060","display_name":"Armin Pirastehzad","orcid":"https://orcid.org/0000-0002-8238-7258"},"institutions":[{"id":"https://openalex.org/I23946033","display_name":"University of Tehran","ror":"https://ror.org/05vf56z40","country_code":"IR","type":"education","lineage":["https://openalex.org/I23946033"]}],"countries":["IR"],"is_corresponding":false,"raw_author_name":"Armin Pirastehzad","raw_affiliation_strings":["School of Electrical and Computer Engineering, University of Tehran, Tehran, Iran"],"raw_orcid":"https://orcid.org/0000-0002-8238-7258","affiliations":[{"raw_affiliation_string":"School of Electrical and Computer Engineering, University of Tehran, Tehran, Iran","institution_ids":["https://openalex.org/I23946033"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5086648677","display_name":"Mohammad Javad Yazdanpanah","orcid":"https://orcid.org/0000-0001-7098-8331"},"institutions":[{"id":"https://openalex.org/I23946033","display_name":"University of Tehran","ror":"https://ror.org/05vf56z40","country_code":"IR","type":"education","lineage":["https://openalex.org/I23946033"]}],"countries":["IR"],"is_corresponding":false,"raw_author_name":"Mohammad Javad Yazdanpanah","raw_affiliation_strings":["Control and Intelligent Processing Center of Excellence, School of Electrical and Computer Engineering, University of Tehran, Tehran, Iran"],"raw_orcid":"https://orcid.org/0000-0001-7098-8331","affiliations":[{"raw_affiliation_string":"Control and Intelligent Processing Center of Excellence, School of Electrical and Computer Engineering, University of Tehran, Tehran, Iran","institution_ids":["https://openalex.org/I23946033"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I23946033"],"apc_list":null,"apc_paid":null,"fwci":1.2289,"has_fulltext":false,"cited_by_count":5,"citation_normalized_percentile":{"value":0.75697302,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"67","issue":"4","first_page":"1760","last_page":"1775"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11416","display_name":"Numerical methods for differential equations","score":0.9998999834060669,"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":0.9998999834060669,"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/T11206","display_name":"Model Reduction and Neural Networks","score":0.9979000091552734,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10173","display_name":"Computational Fluid Dynamics and Aerodynamics","score":0.9957000017166138,"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":0.7262688279151917},{"id":"https://openalex.org/keywords/gauss-pseudospectral-method","display_name":"Gauss pseudospectral method","score":0.5922396779060364},{"id":"https://openalex.org/keywords/pseudospectral-optimal-control","display_name":"Pseudospectral optimal control","score":0.5645521879196167},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.4968138039112091},{"id":"https://openalex.org/keywords/collocation-method","display_name":"Collocation method","score":0.47603681683540344},{"id":"https://openalex.org/keywords/approximation-error","display_name":"Approximation error","score":0.4701388478279114},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.46799251437187195},{"id":"https://openalex.org/keywords/collocation","display_name":"Collocation (remote sensing)","score":0.44645464420318604},{"id":"https://openalex.org/keywords/pseudo-spectral-method","display_name":"Pseudo-spectral method","score":0.41935232281684875},{"id":"https://openalex.org/keywords/fourier-transform","display_name":"Fourier transform","score":0.35486242175102234},{"id":"https://openalex.org/keywords/fourier-analysis","display_name":"Fourier analysis","score":0.22491464018821716},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.19592347741127014},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.11363238096237183}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7262688279151917},{"id":"https://openalex.org/C71026131","wikidata":"https://www.wikidata.org/wiki/Q5527825","display_name":"Gauss pseudospectral method","level":5,"score":0.5922396779060364},{"id":"https://openalex.org/C154304650","wikidata":"https://www.wikidata.org/wiki/Q7255577","display_name":"Pseudospectral optimal control","level":5,"score":0.5645521879196167},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4968138039112091},{"id":"https://openalex.org/C2126413","wikidata":"https://www.wikidata.org/wiki/Q1779479","display_name":"Collocation method","level":4,"score":0.47603681683540344},{"id":"https://openalex.org/C122383733","wikidata":"https://www.wikidata.org/wiki/Q865920","display_name":"Approximation error","level":2,"score":0.4701388478279114},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.46799251437187195},{"id":"https://openalex.org/C80023036","wikidata":"https://www.wikidata.org/wiki/Q5147531","display_name":"Collocation (remote sensing)","level":2,"score":0.44645464420318604},{"id":"https://openalex.org/C177937620","wikidata":"https://www.wikidata.org/wiki/Q7254447","display_name":"Pseudo-spectral method","level":4,"score":0.41935232281684875},{"id":"https://openalex.org/C102519508","wikidata":"https://www.wikidata.org/wiki/Q6520159","display_name":"Fourier transform","level":2,"score":0.35486242175102234},{"id":"https://openalex.org/C203024314","wikidata":"https://www.wikidata.org/wiki/Q1365258","display_name":"Fourier analysis","level":3,"score":0.22491464018821716},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.19592347741127014},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.11363238096237183},{"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/C51544822","wikidata":"https://www.wikidata.org/wiki/Q465274","display_name":"Ordinary differential equation","level":3,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tac.2021.3079185","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tac.2021.3079185","pdf_url":null,"source":{"id":"https://openalex.org/S184954342","display_name":"IEEE Transactions on Automatic Control","issn_l":"0018-9286","issn":["0018-9286","1558-2523","2334-3303"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Automatic Control","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":40,"referenced_works":["https://openalex.org/W62529199","https://openalex.org/W114979488","https://openalex.org/W1627568958","https://openalex.org/W1967353213","https://openalex.org/W2005262540","https://openalex.org/W2017048119","https://openalex.org/W2028454169","https://openalex.org/W2045453705","https://openalex.org/W2055035157","https://openalex.org/W2056773491","https://openalex.org/W2059912234","https://openalex.org/W2063457282","https://openalex.org/W2087096407","https://openalex.org/W2089440813","https://openalex.org/W2091402587","https://openalex.org/W2114781747","https://openalex.org/W2127915327","https://openalex.org/W2137755184","https://openalex.org/W2140000341","https://openalex.org/W2145682786","https://openalex.org/W2162742731","https://openalex.org/W2164671674","https://openalex.org/W2216369207","https://openalex.org/W2291361416","https://openalex.org/W2318887823","https://openalex.org/W2411487419","https://openalex.org/W2507764754","https://openalex.org/W2561326484","https://openalex.org/W2613164457","https://openalex.org/W2613611597","https://openalex.org/W2745168490","https://openalex.org/W2766000188","https://openalex.org/W2995147317","https://openalex.org/W3010176051","https://openalex.org/W3160954918","https://openalex.org/W4213367573","https://openalex.org/W4247375400","https://openalex.org/W4249919931","https://openalex.org/W4254900683","https://openalex.org/W4293079218"],"related_works":["https://openalex.org/W2550657075","https://openalex.org/W1512809069","https://openalex.org/W2761671048","https://openalex.org/W2357738898","https://openalex.org/W2281601070","https://openalex.org/W2143234151","https://openalex.org/W2356744059","https://openalex.org/W1974501530","https://openalex.org/W4387187495","https://openalex.org/W2069381275"],"abstract_inverted_index":{"Through":[0],"the":[1,17,35,41,49,63,78,82,86,96,104],"combination":[2],"of":[3,19,22,38,52,85,119],"contraction":[4],"mapping":[5],"and":[6,28,77,112],"pseudospectral":[7],"method,":[8],"we":[9,102],"propose":[10],"a":[11,20,53,116],"successive":[12],"approximation":[13,105],"technique":[14],"to":[15],"approximate":[16,83],"solution":[18,84],"class":[21],"regulator":[23],"equations":[24],"with":[25,73],"periodic":[26],"exosystems":[27],"hyperbolic":[29],"zero":[30],"dynamics.":[31],"In":[32],"this":[33],"scheme,":[34],"initial":[36],"points":[37],"flows":[39,58],"on":[40],"zero-error":[42],"constrained":[43],"manifolds":[44],"are":[45,59],"approximated":[46],"successively":[47],"as":[48,101],"fixed":[50],"point":[51],"contractive":[54],"integral":[55],"mapping.":[56],"Accordingly,":[57],"obtained":[60],"by":[61],"utilizing":[62],"scaled":[64],"Fourier\u2013Gauss\u2013Radau":[65],"collocation":[66],"method.":[67],"Appropriate":[68],"error":[69,76,79,98],"analysis,":[70],"in":[71],"association":[72],"both":[74],"regulation":[75,97],"resulting":[80],"from":[81],"center":[87],"manifold":[88],"equation,":[89],"is":[90],"provided.":[91],"Our":[92],"analysis":[93],"shows":[94],"that":[95],"becomes":[99],"negligible":[100],"start":[103],"process":[106],"at":[107],"an":[108],"adequately":[109],"large":[110],"order":[111],"maintain":[113],"it":[114],"for":[115],"proper":[117],"number":[118],"iterations.":[120]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
