{"id":"https://openalex.org/W2140630087","doi":"https://doi.org/10.1093/imamci/dnr018","title":"Solving a class of linear and non-linear optimal control problems by homotopy perturbation method","display_name":"Solving a class of linear and non-linear optimal control problems by homotopy perturbation method","publication_year":2011,"publication_date":"2011-12-01","ids":{"openalex":"https://openalex.org/W2140630087","doi":"https://doi.org/10.1093/imamci/dnr018","mag":"2140630087"},"language":"en","primary_location":{"id":"doi:10.1093/imamci/dnr018","is_oa":false,"landing_page_url":"https://doi.org/10.1093/imamci/dnr018","pdf_url":null,"source":{"id":"https://openalex.org/S162756791","display_name":"IMA Journal of Mathematical Control and Information","issn_l":"0265-0754","issn":["0265-0754","1471-6887"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311648","host_organization_name":"Oxford University Press","host_organization_lineage":["https://openalex.org/P4310311648","https://openalex.org/P4310311647"],"host_organization_lineage_names":["Oxford University Press","University of Oxford"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IMA Journal of Mathematical Control and Information","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/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":true,"raw_author_name":"S. Effati","raw_affiliation_strings":["Department of Applied Mathematics, Ferdowsi University of Mashhad, Mashhad, Iran","Department of Applied Mathematics , Ferdowsi University of Mashhad , Mashhad , IRAN"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics, Ferdowsi University of Mashhad, Mashhad, Iran","institution_ids":["https://openalex.org/I86958956"]},{"raw_affiliation_string":"Department of Applied Mathematics , Ferdowsi University of Mashhad , Mashhad , IRAN","institution_ids":["https://openalex.org/I86958956"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5002469157","display_name":"Hassan Saberi Nik","orcid":"https://orcid.org/0000-0003-2521-1325"},"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":"H. S. Nik","raw_affiliation_strings":["Department of Applied Mathematics, Ferdowsi University of Mashhad, Mashhad, Iran","Department of Applied Mathematics , Ferdowsi University of Mashhad , Mashhad , IRAN"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics, Ferdowsi University of Mashhad, Mashhad, Iran","institution_ids":["https://openalex.org/I86958956"]},{"raw_affiliation_string":"Department of Applied Mathematics , Ferdowsi University of Mashhad , Mashhad , IRAN","institution_ids":["https://openalex.org/I86958956"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5021656896"],"corresponding_institution_ids":["https://openalex.org/I86958956"],"apc_list":{"value":2582,"currency":"GBP","value_usd":3167},"apc_paid":null,"fwci":3.3353,"has_fulltext":false,"cited_by_count":33,"citation_normalized_percentile":{"value":0.91255097,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"28","issue":"4","first_page":"539","last_page":"553"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10288","display_name":"Fractional Differential Equations Solutions","score":1.0,"subfield":{"id":"https://openalex.org/subfields/2611","display_name":"Modeling and Simulation"},"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/T10288","display_name":"Fractional Differential Equations Solutions","score":1.0,"subfield":{"id":"https://openalex.org/subfields/2611","display_name":"Modeling and Simulation"},"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/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9882000088691711,"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/T10541","display_name":"Nonlinear Differential Equations Analysis","score":0.9860000014305115,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/homotopy-perturbation-method","display_name":"Homotopy perturbation method","score":0.6722995042800903},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.5852909684181213},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5119351148605347},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.43481916189193726},{"id":"https://openalex.org/keywords/perturbation","display_name":"Perturbation (astronomy)","score":0.4255087375640869},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.38697904348373413},{"id":"https://openalex.org/keywords/mathematics-education","display_name":"Mathematics education","score":0.37504637241363525},{"id":"https://openalex.org/keywords/homotopy","display_name":"Homotopy","score":0.3295345604419708},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.20465901494026184},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.13829556107521057},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.06811299920082092}],"concepts":[{"id":"https://openalex.org/C91328119","wikidata":"https://www.wikidata.org/wiki/Q17030668","display_name":"Homotopy perturbation method","level":3,"score":0.6722995042800903},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.5852909684181213},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5119351148605347},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.43481916189193726},{"id":"https://openalex.org/C177918212","wikidata":"https://www.wikidata.org/wiki/Q803623","display_name":"Perturbation (astronomy)","level":2,"score":0.4255087375640869},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.38697904348373413},{"id":"https://openalex.org/C145420912","wikidata":"https://www.wikidata.org/wiki/Q853077","display_name":"Mathematics education","level":1,"score":0.37504637241363525},{"id":"https://openalex.org/C5961521","wikidata":"https://www.wikidata.org/wiki/Q746083","display_name":"Homotopy","level":2,"score":0.3295345604419708},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.20465901494026184},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.13829556107521057},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.06811299920082092},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1093/imamci/dnr018","is_oa":false,"landing_page_url":"https://doi.org/10.1093/imamci/dnr018","pdf_url":null,"source":{"id":"https://openalex.org/S162756791","display_name":"IMA Journal of Mathematical Control and Information","issn_l":"0265-0754","issn":["0265-0754","1471-6887"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311648","host_organization_name":"Oxford University Press","host_organization_lineage":["https://openalex.org/P4310311648","https://openalex.org/P4310311647"],"host_organization_lineage_names":["Oxford University Press","University of Oxford"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IMA Journal of Mathematical Control and Information","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":21,"referenced_works":["https://openalex.org/W47669410","https://openalex.org/W342570390","https://openalex.org/W357773498","https://openalex.org/W1568666422","https://openalex.org/W1843832723","https://openalex.org/W1983178975","https://openalex.org/W1983859989","https://openalex.org/W1990438185","https://openalex.org/W1994662646","https://openalex.org/W1996618278","https://openalex.org/W2002138473","https://openalex.org/W2003806194","https://openalex.org/W2007579839","https://openalex.org/W2009343239","https://openalex.org/W2015256935","https://openalex.org/W2024673010","https://openalex.org/W2039823633","https://openalex.org/W2060601511","https://openalex.org/W2061719497","https://openalex.org/W2115529165","https://openalex.org/W2165917005"],"related_works":["https://openalex.org/W2461502133","https://openalex.org/W1982459877","https://openalex.org/W2993712719","https://openalex.org/W2077317900","https://openalex.org/W1998530100","https://openalex.org/W4312711876","https://openalex.org/W4294997313","https://openalex.org/W2312258530","https://openalex.org/W144943869","https://openalex.org/W3097502974"],"abstract_inverted_index":{"In":[0],"this":[1],"paper,":[2],"we":[3],"give":[4],"an":[5],"analytical":[6],"approximate":[7],"solution":[8],"for":[9],"non-linear":[10,31,83],"quadratic":[11],"optimal":[12,16,67,72],"control":[13,17,68],"problems":[14],"and":[15,36,70,85,95],"of":[18,50,77,97],"linear":[19,37,51,57,87],"systems":[20],"using":[21],"the":[22,28,30,41,55,66,71,75,93,98],"homotopy":[23],"perturbation":[24],"method":[25],"(HPM).":[26],"Applying":[27],"HPM,":[29],"two-point":[32],"boundary-value":[33],"problem":[34],"(TPBVP)":[35],"systems,":[38],"derived":[39],"from":[40],"Pontryagin's":[42],"maximum":[43],"principle,":[44],"are":[45,89],"transformed":[46],"into":[47],"a":[48,61,82],"sequence":[49,59],"time-invariant":[52],"TPBVP\u2019s.":[53],"Solving":[54],"proposed":[56,99],"TPBVP":[58],"in":[60,74],"recursive":[62],"manner":[63],"leads":[64],"to":[65,91],"law":[69],"trajectory":[73],"form":[76],"rapid":[78],"convergent":[79],"series.":[80],"Finally,":[81],"example":[84],"several":[86],"examples":[88],"given":[90],"verify":[92],"reliability":[94],"efficiency":[96],"method.":[100]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":4},{"year":2014,"cited_by_count":4},{"year":2013,"cited_by_count":7},{"year":2012,"cited_by_count":3}],"updated_date":"2026-06-16T07:32:37.131356","created_date":"2025-10-10T00:00:00"}
