{"id":"https://openalex.org/W4285154334","doi":"https://doi.org/10.1093/imamci/dnac010","title":"First-order and second-order necessary optimality conditions for discrete-time stochastic systems with delay","display_name":"First-order and second-order necessary optimality conditions for discrete-time stochastic systems with delay","publication_year":2022,"publication_date":"2022-04-29","ids":{"openalex":"https://openalex.org/W4285154334","doi":"https://doi.org/10.1093/imamci/dnac010"},"language":"en","primary_location":{"id":"doi:10.1093/imamci/dnac010","is_oa":false,"landing_page_url":"https://doi.org/10.1093/imamci/dnac010","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/A5017793990","display_name":"Teng Song","orcid":"https://orcid.org/0000-0002-2045-2894"},"institutions":[{"id":"https://openalex.org/I196699116","display_name":"Wuhan University of Technology","ror":"https://ror.org/03fe7t173","country_code":"CN","type":"education","lineage":["https://openalex.org/I196699116"]},{"id":"https://openalex.org/I37461747","display_name":"Wuhan University","ror":"https://ror.org/033vjfk17","country_code":"CN","type":"education","lineage":["https://openalex.org/I37461747"]},{"id":"https://openalex.org/I4210100789","display_name":"Wuhan College","ror":"https://ror.org/01dashf18","country_code":"CN","type":"nonprofit","lineage":["https://openalex.org/I4210100789"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Teng Song","raw_affiliation_strings":["School of Science , , 430070 Wuhan , P R China","Wuhan University of Technology , , 430070 Wuhan , P R China","School of Science, Wuhan University of Technology, 430070 Wuhan, P R China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Science , , 430070 Wuhan , P R China","institution_ids":["https://openalex.org/I4210100789","https://openalex.org/I37461747"]},{"raw_affiliation_string":"Wuhan University of Technology , , 430070 Wuhan , P R China","institution_ids":["https://openalex.org/I196699116"]},{"raw_affiliation_string":"School of Science, Wuhan University of Technology, 430070 Wuhan, P R China","institution_ids":["https://openalex.org/I196699116"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100395509","display_name":"Bin Liu","orcid":"https://orcid.org/0000-0002-5852-7599"},"institutions":[{"id":"https://openalex.org/I47720641","display_name":"Huazhong University of Science and Technology","ror":"https://ror.org/00p991c53","country_code":"CN","type":"education","lineage":["https://openalex.org/I47720641"]},{"id":"https://openalex.org/I75900474","display_name":"Hubei University","ror":"https://ror.org/03a60m280","country_code":"CN","type":"education","lineage":["https://openalex.org/I75900474"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Bin Liu","raw_affiliation_strings":["Huazhong University of Science and Technology , Hubei Key Laboratory of Engineering Modeling and Scientific Computing, , 430074 Wuhan , P R China","School of Mathematics and Statistics , Hubei Key Laboratory of Engineering Modeling and Scientific Computing, , 430074 Wuhan , P R China","School of Mathematics and Statistics, Hubei Key Laboratory of Engineering Modeling and Scientific Computing, Huazhong University of Science and Technology, 430074 Wuhan, P R China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Huazhong University of Science and Technology , Hubei Key Laboratory of Engineering Modeling and Scientific Computing, , 430074 Wuhan , P R China","institution_ids":["https://openalex.org/I47720641"]},{"raw_affiliation_string":"School of Mathematics and Statistics , Hubei Key Laboratory of Engineering Modeling and Scientific Computing, , 430074 Wuhan , P R China","institution_ids":["https://openalex.org/I75900474"]},{"raw_affiliation_string":"School of Mathematics and Statistics, Hubei Key Laboratory of Engineering Modeling and Scientific Computing, Huazhong University of Science and Technology, 430074 Wuhan, P R China","institution_ids":["https://openalex.org/I47720641"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5100395509"],"corresponding_institution_ids":["https://openalex.org/I47720641","https://openalex.org/I75900474"],"apc_list":{"value":2582,"currency":"GBP","value_usd":3167},"apc_paid":null,"fwci":0.1213,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.40533083,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"39","issue":"2","first_page":"731","last_page":"750"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10046","display_name":"Stability and Control of Uncertain Systems","score":0.9915000200271606,"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/T10046","display_name":"Stability and Control of Uncertain Systems","score":0.9915000200271606,"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/T10067","display_name":"Stochastic processes and financial applications","score":0.9890999794006348,"subfield":{"id":"https://openalex.org/subfields/2003","display_name":"Finance"},"field":{"id":"https://openalex.org/fields/20","display_name":"Economics, Econometrics and Finance"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T10545","display_name":"Optimization and Variational Analysis","score":0.9857000112533569,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/pointwise","display_name":"Pointwise","score":0.7856099009513855},{"id":"https://openalex.org/keywords/discrete-time-and-continuous-time","display_name":"Discrete time and continuous time","score":0.7443424463272095},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6622136831283569},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.5691705942153931},{"id":"https://openalex.org/keywords/discrete-time-stochastic-process","display_name":"Discrete-time stochastic process","score":0.5266494750976562},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.495444655418396},{"id":"https://openalex.org/keywords/continuous-time-stochastic-process","display_name":"Continuous-time stochastic process","score":0.4134214222431183},{"id":"https://openalex.org/keywords/stochastic-control","display_name":"Stochastic control","score":0.4132646322250366},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.32387590408325195},{"id":"https://openalex.org/keywords/optimal-control","display_name":"Optimal control","score":0.3121432662010193},{"id":"https://openalex.org/keywords/stochastic-differential-equation","display_name":"Stochastic differential equation","score":0.2470007836818695},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.16206884384155273}],"concepts":[{"id":"https://openalex.org/C2777984123","wikidata":"https://www.wikidata.org/wiki/Q9248237","display_name":"Pointwise","level":2,"score":0.7856099009513855},{"id":"https://openalex.org/C55689738","wikidata":"https://www.wikidata.org/wiki/Q15963867","display_name":"Discrete time and continuous time","level":2,"score":0.7443424463272095},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6622136831283569},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.5691705942153931},{"id":"https://openalex.org/C92703954","wikidata":"https://www.wikidata.org/wiki/Q176737","display_name":"Discrete-time stochastic process","level":4,"score":0.5266494750976562},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.495444655418396},{"id":"https://openalex.org/C158535547","wikidata":"https://www.wikidata.org/wiki/Q5165437","display_name":"Continuous-time stochastic process","level":3,"score":0.4134214222431183},{"id":"https://openalex.org/C170131372","wikidata":"https://www.wikidata.org/wiki/Q7617811","display_name":"Stochastic control","level":3,"score":0.4132646322250366},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.32387590408325195},{"id":"https://openalex.org/C91575142","wikidata":"https://www.wikidata.org/wiki/Q1971426","display_name":"Optimal control","level":2,"score":0.3121432662010193},{"id":"https://openalex.org/C51955184","wikidata":"https://www.wikidata.org/wiki/Q1545585","display_name":"Stochastic differential equation","level":2,"score":0.2470007836818695},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.16206884384155273},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"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:10.1093/imamci/dnac010","is_oa":false,"landing_page_url":"https://doi.org/10.1093/imamci/dnac010","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":[{"id":"https://openalex.org/G5379842206","display_name":"\u65f6\u6ede\u751f\u7269\u504f\u5fae\u5206\u7cfb\u7edf\u6700\u4f18\u63a7\u5236\u82e5\u5e72\u95ee\u9898\u7814\u7a76","funder_award_id":"11971185","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":22,"referenced_works":["https://openalex.org/W2005864397","https://openalex.org/W2020203578","https://openalex.org/W2034200236","https://openalex.org/W2047250515","https://openalex.org/W2068168851","https://openalex.org/W2078215229","https://openalex.org/W2111048679","https://openalex.org/W2166893324","https://openalex.org/W2334591577","https://openalex.org/W2473255728","https://openalex.org/W2622257677","https://openalex.org/W2785271143","https://openalex.org/W2803493377","https://openalex.org/W2890074057","https://openalex.org/W2910817715","https://openalex.org/W2912324827","https://openalex.org/W2916519506","https://openalex.org/W2958736805","https://openalex.org/W2962934438","https://openalex.org/W2962959889","https://openalex.org/W3161609309","https://openalex.org/W4212780424"],"related_works":["https://openalex.org/W2912324827","https://openalex.org/W1515213997","https://openalex.org/W3109286255","https://openalex.org/W2138230037","https://openalex.org/W4302305711","https://openalex.org/W2949098703","https://openalex.org/W2121345901","https://openalex.org/W4299533968","https://openalex.org/W2963556112","https://openalex.org/W2126102075"],"abstract_inverted_index":{"Abstract":[0],"This":[1],"paper":[2],"is":[3],"concerned":[4],"with":[5,17],"the":[6,35,58,66],"first-order":[7],"and":[8,27,41,65],"second-order":[9,68],"necessary":[10,43,59],"optimality":[11,44,60,69],"conditions":[12],"for":[13],"discrete-time":[14,29,37,50],"stochastic":[15,31,38,52],"systems":[16],"delay":[18],"under":[19],"weak":[20],"assumptions.":[21],"Based":[22],"on":[23],"a":[24,28,48],"characteristic":[25],"method":[26],"backward":[30,51],"equation,":[32,54],"we":[33,55],"establish":[34],"linearized":[36],"maximum":[39],"principle":[40],"Euler-type":[42],"condition.":[45,70],"Moreover,":[46],"by":[47],"new":[49],"matrix":[53],"also":[56],"obtain":[57],"condition":[61],"of":[62],"quasi-singular":[63],"control":[64],"pointwise":[67]},"counts_by_year":[{"year":2023,"cited_by_count":1}],"updated_date":"2026-06-06T09:05:17.133730","created_date":"2025-10-10T00:00:00"}