{"id":"https://openalex.org/W2027667684","doi":"https://doi.org/10.1631/jzus.c1000325","title":"Solving infinite horizon nonlinear optimal control problems using an extended modal series method","display_name":"Solving infinite horizon nonlinear optimal control problems using an extended modal series method","publication_year":2011,"publication_date":"2011-08-01","ids":{"openalex":"https://openalex.org/W2027667684","doi":"https://doi.org/10.1631/jzus.c1000325","mag":"2027667684"},"language":"en","primary_location":{"id":"doi:10.1631/jzus.c1000325","is_oa":false,"landing_page_url":"https://doi.org/10.1631/jzus.c1000325","pdf_url":null,"source":{"id":"https://openalex.org/S199067057","display_name":"Frontiers of Information Technology & Electronic Engineering","issn_l":"1869-1951","issn":["1869-1951","1869-196X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311937","host_organization_name":"Zhejiang University Press","host_organization_lineage":["https://openalex.org/P4310311937"],"host_organization_lineage_names":["Zhejiang University Press"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Zhejiang University SCIENCE C","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/A5033927734","display_name":"Amin Jajarmi","orcid":"https://orcid.org/0000-0003-2768-840X"},"institutions":[{"id":"https://openalex.org/I86958956","display_name":"Ferdowsi University of Mashhad","ror":"https://ror.org/00g6ka752","country_code":"IR","type":"education","lineage":["https://openalex.org/I86958956"]}],"countries":["IR"],"is_corresponding":true,"raw_author_name":"Amin Jajarmi","raw_affiliation_strings":["Advanced Control and Nonlinear Laboratory, Department of Electrical Engineering, Ferdowsi University of Mashhad, Mashhad, Iran","Ferdowsi University of Mashhad"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Advanced Control and Nonlinear Laboratory, Department of Electrical Engineering, Ferdowsi University of Mashhad, Mashhad, Iran","institution_ids":["https://openalex.org/I86958956"]},{"raw_affiliation_string":"Ferdowsi University of Mashhad","institution_ids":["https://openalex.org/I86958956"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5056660688","display_name":"Naser Pariz","orcid":"https://orcid.org/0000-0001-6689-9176"},"institutions":[{"id":"https://openalex.org/I86958956","display_name":"Ferdowsi University of Mashhad","ror":"https://ror.org/00g6ka752","country_code":"IR","type":"education","lineage":["https://openalex.org/I86958956"]}],"countries":["IR"],"is_corresponding":false,"raw_author_name":"Naser Pariz","raw_affiliation_strings":["Advanced Control and Nonlinear Laboratory, Department of Electrical Engineering, Ferdowsi University of Mashhad, Mashhad, Iran","Ferdowsi University of Mashhad"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Advanced Control and Nonlinear Laboratory, Department of Electrical Engineering, Ferdowsi University of Mashhad, Mashhad, Iran","institution_ids":["https://openalex.org/I86958956"]},{"raw_affiliation_string":"Ferdowsi University of Mashhad","institution_ids":["https://openalex.org/I86958956"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5021656896","display_name":"Sohrab Effati","orcid":"https://orcid.org/0000-0001-9752-0034"},"institutions":[{"id":"https://openalex.org/I86958956","display_name":"Ferdowsi University of Mashhad","ror":"https://ror.org/00g6ka752","country_code":"IR","type":"education","lineage":["https://openalex.org/I86958956"]}],"countries":["IR"],"is_corresponding":false,"raw_author_name":"Sohrab Effati","raw_affiliation_strings":["Department of Applied Mathematics, Faculty of Mathematical Sciences, Ferdowsi University of Mashhad, Mashhad, Iran","Ferdowsi University of Mashhad"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics, Faculty of Mathematical Sciences, Ferdowsi University of Mashhad, Mashhad, Iran","institution_ids":["https://openalex.org/I86958956"]},{"raw_affiliation_string":"Ferdowsi University of Mashhad","institution_ids":["https://openalex.org/I86958956"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5037127708","display_name":"Ali Vahidian Kamyad","orcid":"https://orcid.org/0000-0001-5127-0690"},"institutions":[{"id":"https://openalex.org/I86958956","display_name":"Ferdowsi University of Mashhad","ror":"https://ror.org/00g6ka752","country_code":"IR","type":"education","lineage":["https://openalex.org/I86958956"]}],"countries":["IR"],"is_corresponding":false,"raw_author_name":"Ali Vahidian Kamyad","raw_affiliation_strings":["Ferdowsi University of Mashhad"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Ferdowsi University of Mashhad","institution_ids":["https://openalex.org/I86958956"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5033927734"],"corresponding_institution_ids":["https://openalex.org/I86958956"],"apc_list":null,"apc_paid":null,"fwci":1.1917,"has_fulltext":false,"cited_by_count":23,"citation_normalized_percentile":{"value":0.78484451,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"12","issue":"8","first_page":"667","last_page":"677"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12794","display_name":"Adaptive Dynamic Programming Control","score":0.9921000003814697,"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"}},"topics":[{"id":"https://openalex.org/T12794","display_name":"Adaptive Dynamic Programming Control","score":0.9921000003814697,"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"}},{"id":"https://openalex.org/T10545","display_name":"Optimization and Variational Analysis","score":0.9729999899864197,"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"}},{"id":"https://openalex.org/T12277","display_name":"Frequency Control in Power Systems","score":0.9638000130653381,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic 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/optimal-control","display_name":"Optimal control","score":0.7590941190719604},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.6793982982635498},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6273208856582642},{"id":"https://openalex.org/keywords/series","display_name":"Series (stratigraphy)","score":0.5945388674736023},{"id":"https://openalex.org/keywords/sequence","display_name":"Sequence (biology)","score":0.5477095246315002},{"id":"https://openalex.org/keywords/modal","display_name":"Modal","score":0.4970076382160187},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.479410856962204},{"id":"https://openalex.org/keywords/maximum-principle","display_name":"Maximum principle","score":0.47571736574172974},{"id":"https://openalex.org/keywords/ordinary-differential-equation","display_name":"Ordinary differential equation","score":0.4684726297855377},{"id":"https://openalex.org/keywords/trajectory","display_name":"Trajectory","score":0.4467242956161499},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4358086585998535},{"id":"https://openalex.org/keywords/convergent-series","display_name":"Convergent series","score":0.43496420979499817},{"id":"https://openalex.org/keywords/boundary-value-problem","display_name":"Boundary value problem","score":0.42390304803848267},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.4231681823730469},{"id":"https://openalex.org/keywords/rate-of-convergence","display_name":"Rate of convergence","score":0.42053383588790894},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.3604235351085663},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.34390464425086975},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.32209938764572144},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.21015429496765137},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.17642313241958618},{"id":"https://openalex.org/keywords/power-series","display_name":"Power series","score":0.06913337111473083}],"concepts":[{"id":"https://openalex.org/C91575142","wikidata":"https://www.wikidata.org/wiki/Q1971426","display_name":"Optimal control","level":2,"score":0.7590941190719604},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.6793982982635498},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6273208856582642},{"id":"https://openalex.org/C143724316","wikidata":"https://www.wikidata.org/wiki/Q312468","display_name":"Series (stratigraphy)","level":2,"score":0.5945388674736023},{"id":"https://openalex.org/C2778112365","wikidata":"https://www.wikidata.org/wiki/Q3511065","display_name":"Sequence (biology)","level":2,"score":0.5477095246315002},{"id":"https://openalex.org/C71139939","wikidata":"https://www.wikidata.org/wiki/Q910194","display_name":"Modal","level":2,"score":0.4970076382160187},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.479410856962204},{"id":"https://openalex.org/C31010330","wikidata":"https://www.wikidata.org/wiki/Q1914255","display_name":"Maximum principle","level":3,"score":0.47571736574172974},{"id":"https://openalex.org/C51544822","wikidata":"https://www.wikidata.org/wiki/Q465274","display_name":"Ordinary differential equation","level":3,"score":0.4684726297855377},{"id":"https://openalex.org/C13662910","wikidata":"https://www.wikidata.org/wiki/Q193139","display_name":"Trajectory","level":2,"score":0.4467242956161499},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4358086585998535},{"id":"https://openalex.org/C1115519","wikidata":"https://www.wikidata.org/wiki/Q1211057","display_name":"Convergent series","level":3,"score":0.43496420979499817},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.42390304803848267},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.4231681823730469},{"id":"https://openalex.org/C57869625","wikidata":"https://www.wikidata.org/wiki/Q1783502","display_name":"Rate of convergence","level":3,"score":0.42053383588790894},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.3604235351085663},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.34390464425086975},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.32209938764572144},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.21015429496765137},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.17642313241958618},{"id":"https://openalex.org/C73905626","wikidata":"https://www.wikidata.org/wiki/Q206925","display_name":"Power series","level":2,"score":0.06913337111473083},{"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/C127162648","wikidata":"https://www.wikidata.org/wiki/Q16858953","display_name":"Channel (broadcasting)","level":2,"score":0.0},{"id":"https://openalex.org/C54355233","wikidata":"https://www.wikidata.org/wiki/Q7162","display_name":"Genetics","level":1,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C1276947","wikidata":"https://www.wikidata.org/wiki/Q333","display_name":"Astronomy","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/C188027245","wikidata":"https://www.wikidata.org/wiki/Q750446","display_name":"Polymer chemistry","level":1,"score":0.0},{"id":"https://openalex.org/C151730666","wikidata":"https://www.wikidata.org/wiki/Q7205","display_name":"Paleontology","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},{"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/C31258907","wikidata":"https://www.wikidata.org/wiki/Q1301371","display_name":"Computer network","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"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:10.1631/jzus.c1000325","is_oa":false,"landing_page_url":"https://doi.org/10.1631/jzus.c1000325","pdf_url":null,"source":{"id":"https://openalex.org/S199067057","display_name":"Frontiers of Information Technology & Electronic Engineering","issn_l":"1869-1951","issn":["1869-1951","1869-196X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311937","host_organization_name":"Zhejiang University Press","host_organization_lineage":["https://openalex.org/P4310311937"],"host_organization_lineage_names":["Zhejiang University Press"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Zhejiang University SCIENCE C","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Peace, Justice and strong institutions","id":"https://metadata.un.org/sdg/16","score":0.7599999904632568}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":32,"referenced_works":["https://openalex.org/W199142884","https://openalex.org/W404241533","https://openalex.org/W1220972283","https://openalex.org/W1568666422","https://openalex.org/W1595032093","https://openalex.org/W1978373919","https://openalex.org/W1983859989","https://openalex.org/W1984041157","https://openalex.org/W1990438185","https://openalex.org/W2024673010","https://openalex.org/W2042994047","https://openalex.org/W2046248406","https://openalex.org/W2047090868","https://openalex.org/W2047470736","https://openalex.org/W2047573454","https://openalex.org/W2054501800","https://openalex.org/W2056653303","https://openalex.org/W2062236853","https://openalex.org/W2078543085","https://openalex.org/W2089703493","https://openalex.org/W2099688022","https://openalex.org/W2115529165","https://openalex.org/W2765068902","https://openalex.org/W2787523326","https://openalex.org/W3141151088","https://openalex.org/W4232399354","https://openalex.org/W4234534407","https://openalex.org/W6608143669","https://openalex.org/W6635666278","https://openalex.org/W6641600112","https://openalex.org/W6677078960","https://openalex.org/W7070336693"],"related_works":["https://openalex.org/W2344465999","https://openalex.org/W2891064742","https://openalex.org/W2124696720","https://openalex.org/W1597420886","https://openalex.org/W2074467366","https://openalex.org/W2028690217","https://openalex.org/W2005362598","https://openalex.org/W3213146639","https://openalex.org/W2055393171","https://openalex.org/W2035087110"],"abstract_inverted_index":{"This":[0],"paper":[1],"presents":[2],"a":[3,8,21,36,47,95,100],"new":[4],"approach":[5],"for":[6,75,113],"solving":[7,76],"class":[9],"of":[10,38,62,128],"infinite":[11],"horizon":[12],"nonlinear":[13,22,115],"optimal":[14,52,57,70],"control":[15,53],"problems":[16,45],"(OCPs).":[17],"In":[18],"this":[19],"approach,":[20,131],"two-point":[23],"boundary":[24],"value":[25],"problem":[26],"(TPBVP),":[27],"derived":[28],"from":[29],"Pontryagin\u2019s":[30],"maximum":[31],"principle,":[32],"is":[33,86],"transformed":[34],"into":[35],"sequence":[37],"linear":[39,77],"time-invariant":[40],"TPBVPs.":[41],"Solving":[42],"the":[43,51,56,60,69,73,114,122,129],"latter":[44],"in":[46,59,137],"recursive":[48],"manner":[49],"provides":[50],"law":[54],"and":[55,94,125],"trajectory":[58],"form":[61],"uniformly":[63],"convergent":[64],"series.":[65],"Hence,":[66],"to":[67,105],"obtain":[68],"solution,":[71],"only":[72,120],"techniques":[74],"ordinary":[78],"differential":[79],"equations":[80],"are":[81,103],"employed.":[82],"An":[83],"efficient":[84],"algorithm":[85],"also":[87,133],"presented,":[88],"which":[89],"has":[90],"low":[91],"computational":[92],"complexity":[93],"fast":[96],"convergence":[97],"rate.":[98],"Just":[99],"few":[101],"iterations":[102],"required":[104],"find":[106],"an":[107],"accurate":[108],"enough":[109],"suboptimal":[110],"trajectory-control":[111],"pair":[112],"OCP.":[116],"The":[117],"results":[118],"not":[119],"demonstrate":[121],"efficiency,":[123],"simplicity,":[124],"high":[126],"accuracy":[127],"suggested":[130],"but":[132],"indicate":[134],"its":[135],"effectiveness":[136],"practical":[138],"use.":[139]},"counts_by_year":[{"year":2020,"cited_by_count":4},{"year":2019,"cited_by_count":3},{"year":2018,"cited_by_count":8},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":2}],"updated_date":"2026-07-31T08:31:51.225901","created_date":"2025-10-10T00:00:00"}
