{"id":"https://openalex.org/W2937974562","doi":"https://doi.org/10.1080/00207179.2019.1600032","title":"Optimal control of nonlinear renewal equation","display_name":"Optimal control of nonlinear renewal equation","publication_year":2019,"publication_date":"2019-03-25","ids":{"openalex":"https://openalex.org/W2937974562","doi":"https://doi.org/10.1080/00207179.2019.1600032","mag":"2937974562"},"language":"en","primary_location":{"id":"doi:10.1080/00207179.2019.1600032","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207179.2019.1600032","pdf_url":null,"source":{"id":"https://openalex.org/S88061139","display_name":"International Journal of Control","issn_l":"0020-7179","issn":["0020-7179","1366-5820"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of 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/A5011842931","display_name":"Bhargav Kumar Kakumani","orcid":"https://orcid.org/0000-0001-6484-5289"},"institutions":[{"id":"https://openalex.org/I94595606","display_name":"TIFR Centre for Applicable Mathematics","ror":"https://ror.org/00dp5a155","country_code":"IN","type":"education","lineage":["https://openalex.org/I11947397","https://openalex.org/I2799351866","https://openalex.org/I3149292468","https://openalex.org/I94595606"]}],"countries":["IN"],"is_corresponding":true,"raw_author_name":"Bhargav Kumar Kakumani","raw_affiliation_strings":["T.I.F.R. Centre for Applicable Mathematics, Bangalore, India"],"affiliations":[{"raw_affiliation_string":"T.I.F.R. Centre for Applicable Mathematics, Bangalore, India","institution_ids":["https://openalex.org/I94595606"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5011842931"],"corresponding_institution_ids":["https://openalex.org/I94595606"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.02810444,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":97,"max":99},"biblio":{"volume":"94","issue":"3","first_page":"570","last_page":"578"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11110","display_name":"Stability and Controllability of Differential Equations","score":0.9994999766349792,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems 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/T11110","display_name":"Stability and Controllability of Differential Equations","score":0.9994999766349792,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems 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/T10194","display_name":"Nonlinear Partial Differential Equations","score":0.9977999925613403,"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"}},{"id":"https://openalex.org/T10541","display_name":"Nonlinear Differential Equations Analysis","score":0.9975000023841858,"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/uniqueness","display_name":"Uniqueness","score":0.800491452217102},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.760482668876648},{"id":"https://openalex.org/keywords/optimal-control","display_name":"Optimal control","score":0.7102514505386353},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.6628644466400146},{"id":"https://openalex.org/keywords/variational-principle","display_name":"Variational principle","score":0.5619307160377502},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.5018417835235596},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5012338161468506},{"id":"https://openalex.org/keywords/cone","display_name":"Cone (formal languages)","score":0.46864718198776245},{"id":"https://openalex.org/keywords/maximum-principle","display_name":"Maximum principle","score":0.412601113319397},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3751499056816101},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.36235862970352173},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3608296811580658},{"id":"https://openalex.org/keywords/calculus","display_name":"Calculus (dental)","score":0.3486226201057434},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.18502435088157654},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.08846166729927063},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.04534783959388733}],"concepts":[{"id":"https://openalex.org/C2777021972","wikidata":"https://www.wikidata.org/wiki/Q22976830","display_name":"Uniqueness","level":2,"score":0.800491452217102},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.760482668876648},{"id":"https://openalex.org/C91575142","wikidata":"https://www.wikidata.org/wiki/Q1971426","display_name":"Optimal control","level":2,"score":0.7102514505386353},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.6628644466400146},{"id":"https://openalex.org/C9259290","wikidata":"https://www.wikidata.org/wiki/Q745215","display_name":"Variational principle","level":2,"score":0.5619307160377502},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.5018417835235596},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5012338161468506},{"id":"https://openalex.org/C30014739","wikidata":"https://www.wikidata.org/wiki/Q5159445","display_name":"Cone (formal languages)","level":2,"score":0.46864718198776245},{"id":"https://openalex.org/C31010330","wikidata":"https://www.wikidata.org/wiki/Q1914255","display_name":"Maximum principle","level":3,"score":0.412601113319397},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3751499056816101},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.36235862970352173},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3608296811580658},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.3486226201057434},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.18502435088157654},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.08846166729927063},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.04534783959388733},{"id":"https://openalex.org/C199343813","wikidata":"https://www.wikidata.org/wiki/Q12128","display_name":"Dentistry","level":1,"score":0.0},{"id":"https://openalex.org/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","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/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1080/00207179.2019.1600032","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207179.2019.1600032","pdf_url":null,"source":{"id":"https://openalex.org/S88061139","display_name":"International Journal of Control","issn_l":"0020-7179","issn":["0020-7179","1366-5820"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Control","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G8405430797","display_name":null,"funder_award_id":"PDF/2017/001305","funder_id":"https://openalex.org/F4320334771","funder_display_name":"Science and Engineering Research Board"}],"funders":[{"id":"https://openalex.org/F4320334771","display_name":"Science and Engineering Research Board","ror":"https://ror.org/03ffdsr55"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":22,"referenced_works":["https://openalex.org/W45444623","https://openalex.org/W64816550","https://openalex.org/W161997657","https://openalex.org/W348312448","https://openalex.org/W1511806896","https://openalex.org/W1540294802","https://openalex.org/W1976217191","https://openalex.org/W1995574098","https://openalex.org/W2012334444","https://openalex.org/W2021312711","https://openalex.org/W2046122270","https://openalex.org/W2061542860","https://openalex.org/W2063521938","https://openalex.org/W2079480934","https://openalex.org/W2083321256","https://openalex.org/W2088158750","https://openalex.org/W2149953019","https://openalex.org/W2163595545","https://openalex.org/W2235415941","https://openalex.org/W2386619899","https://openalex.org/W4238989893","https://openalex.org/W6602654154"],"related_works":["https://openalex.org/W2962746246","https://openalex.org/W1967384683","https://openalex.org/W4292923857","https://openalex.org/W162218241","https://openalex.org/W2618936491","https://openalex.org/W4302321938","https://openalex.org/W4285534277","https://openalex.org/W1989531755","https://openalex.org/W2461927677","https://openalex.org/W2262841177"],"abstract_inverted_index":{"In":[0],"this":[1],"article,":[2],"we":[3,32],"study":[4],"the":[5,26,34,42],"optimal":[6,39],"control":[7,40],"for":[8],"a":[9],"nonlinear":[10],"renewal":[11],"equation":[12],"popularly":[13],"known":[14],"as":[15],"McKendrick\u2013von":[16],"Foerster":[17],"(MV)":[18],"equation.":[19],"We":[20],"establish":[21],"necessary":[22],"optimality":[23],"conditions":[24],"using":[25,41],"concept":[27],"of":[28,38],"normal":[29],"cone.":[30],"Finally,":[31],"prove":[33],"existence":[35],"and":[36],"uniqueness":[37],"Ekeland":[43],"variational":[44],"principle.":[45]},"counts_by_year":[{"year":2026,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}