{"id":"https://openalex.org/W3216225288","doi":"https://doi.org/10.1080/00207721.2021.2004260","title":"LQ control of forward and backward stochastic difference system","display_name":"LQ control of forward and backward stochastic difference system","publication_year":2021,"publication_date":"2021-11-22","ids":{"openalex":"https://openalex.org/W3216225288","doi":"https://doi.org/10.1080/00207721.2021.2004260","mag":"3216225288"},"language":"en","primary_location":{"id":"doi:10.1080/00207721.2021.2004260","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207721.2021.2004260","pdf_url":null,"source":{"id":"https://openalex.org/S129640837","display_name":"International Journal of Systems Science","issn_l":"0020-7721","issn":["0020-7721","1464-5319"],"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 Systems Science","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/A5100354213","display_name":"Shen Zhang","orcid":"https://orcid.org/0000-0003-3988-1442"},"institutions":[{"id":"https://openalex.org/I154099455","display_name":"Shandong University","ror":"https://ror.org/0207yh398","country_code":"CN","type":"education","lineage":["https://openalex.org/I154099455"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Shen Zhang","raw_affiliation_strings":["School of Control Science and Engineering, Shandong University, Jinan, People's Republic of China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Control Science and Engineering, Shandong University, Jinan, People's Republic of China","institution_ids":["https://openalex.org/I154099455"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100768356","display_name":"Juanjuan Xu","orcid":"https://orcid.org/0000-0003-0331-9976"},"institutions":[{"id":"https://openalex.org/I154099455","display_name":"Shandong University","ror":"https://ror.org/0207yh398","country_code":"CN","type":"education","lineage":["https://openalex.org/I154099455"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Juanjuan Xu","raw_affiliation_strings":["School of Control Science and Engineering, Shandong University, Jinan, People's Republic of China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Control Science and Engineering, Shandong University, Jinan, People's Republic of China","institution_ids":["https://openalex.org/I154099455"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5003684805","display_name":"Guangchen Wang","orcid":"https://orcid.org/0000-0002-7767-2476"},"institutions":[{"id":"https://openalex.org/I154099455","display_name":"Shandong University","ror":"https://ror.org/0207yh398","country_code":"CN","type":"education","lineage":["https://openalex.org/I154099455"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Guangchen Wang","raw_affiliation_strings":["School of Control Science and Engineering, Shandong University, Jinan, People's Republic of China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Control Science and Engineering, Shandong University, Jinan, People's Republic of China","institution_ids":["https://openalex.org/I154099455"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5114377900","display_name":"Huanshui Zhang","orcid":"https://orcid.org/0000-0002-8611-7327"},"institutions":[{"id":"https://openalex.org/I80143920","display_name":"Shandong University of Science and Technology","ror":"https://ror.org/04gtjhw98","country_code":"CN","type":"education","lineage":["https://openalex.org/I80143920"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Huanshui Zhang","raw_affiliation_strings":["College of Electrical Engineering and Automation, Shandong University of Science and Technology, Qingdao, People's Republic of China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"College of Electrical Engineering and Automation, Shandong University of Science and Technology, Qingdao, People's Republic of China","institution_ids":["https://openalex.org/I80143920"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5100768356"],"corresponding_institution_ids":["https://openalex.org/I154099455"],"apc_list":null,"apc_paid":null,"fwci":0.1939,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":{"value":0.60672989,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":96},"biblio":{"volume":"53","issue":"7","first_page":"1401","last_page":"1415"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10482","display_name":"Mathematical and Theoretical Epidemiology and Ecology Models","score":0.9409000277519226,"subfield":{"id":"https://openalex.org/subfields/2739","display_name":"Public Health, Environmental and Occupational Health"},"field":{"id":"https://openalex.org/fields/27","display_name":"Medicine"},"domain":{"id":"https://openalex.org/domains/4","display_name":"Health Sciences"}},"topics":[{"id":"https://openalex.org/T10482","display_name":"Mathematical and Theoretical Epidemiology and Ecology Models","score":0.9409000277519226,"subfield":{"id":"https://openalex.org/subfields/2739","display_name":"Public Health, Environmental and Occupational Health"},"field":{"id":"https://openalex.org/fields/27","display_name":"Medicine"},"domain":{"id":"https://openalex.org/domains/4","display_name":"Health Sciences"}},{"id":"https://openalex.org/T10067","display_name":"Stochastic processes and financial applications","score":0.9315000176429749,"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/T10046","display_name":"Stability and Control of Uncertain Systems","score":0.9259999990463257,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8521500825881958},{"id":"https://openalex.org/keywords/riccati-equation","display_name":"Riccati equation","score":0.6887539029121399},{"id":"https://openalex.org/keywords/multiplicative-function","display_name":"Multiplicative function","score":0.6758579611778259},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.541014552116394},{"id":"https://openalex.org/keywords/stochastic-control","display_name":"Stochastic control","score":0.5098294615745544},{"id":"https://openalex.org/keywords/optimal-control","display_name":"Optimal control","score":0.4984910488128662},{"id":"https://openalex.org/keywords/quadratic-equation","display_name":"Quadratic equation","score":0.4852735698223114},{"id":"https://openalex.org/keywords/multiplicative-noise","display_name":"Multiplicative noise","score":0.47556963562965393},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.46583810448646545},{"id":"https://openalex.org/keywords/linear-quadratic-regulator","display_name":"Linear-quadratic regulator","score":0.45003458857536316},{"id":"https://openalex.org/keywords/algebraic-riccati-equation","display_name":"Algebraic Riccati equation","score":0.425525963306427},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.3929322361946106},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.2979002296924591},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.24849054217338562},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.14940589666366577},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.09911978244781494}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8521500825881958},{"id":"https://openalex.org/C45473103","wikidata":"https://www.wikidata.org/wiki/Q851503","display_name":"Riccati equation","level":3,"score":0.6887539029121399},{"id":"https://openalex.org/C42747912","wikidata":"https://www.wikidata.org/wiki/Q1048447","display_name":"Multiplicative function","level":2,"score":0.6758579611778259},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.541014552116394},{"id":"https://openalex.org/C170131372","wikidata":"https://www.wikidata.org/wiki/Q7617811","display_name":"Stochastic control","level":3,"score":0.5098294615745544},{"id":"https://openalex.org/C91575142","wikidata":"https://www.wikidata.org/wiki/Q1971426","display_name":"Optimal control","level":2,"score":0.4984910488128662},{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.4852735698223114},{"id":"https://openalex.org/C18015164","wikidata":"https://www.wikidata.org/wiki/Q6935000","display_name":"Multiplicative noise","level":5,"score":0.47556963562965393},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.46583810448646545},{"id":"https://openalex.org/C98779006","wikidata":"https://www.wikidata.org/wiki/Q2520550","display_name":"Linear-quadratic regulator","level":3,"score":0.45003458857536316},{"id":"https://openalex.org/C13847129","wikidata":"https://www.wikidata.org/wiki/Q4723989","display_name":"Algebraic Riccati equation","level":4,"score":0.425525963306427},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.3929322361946106},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.2979002296924591},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.24849054217338562},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.14940589666366577},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.09911978244781494},{"id":"https://openalex.org/C84462506","wikidata":"https://www.wikidata.org/wiki/Q173142","display_name":"Digital signal processing","level":2,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C13412647","wikidata":"https://www.wikidata.org/wiki/Q174948","display_name":"Analog signal","level":3,"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/C9390403","wikidata":"https://www.wikidata.org/wiki/Q3966","display_name":"Computer hardware","level":1,"score":0.0},{"id":"https://openalex.org/C131021393","wikidata":"https://www.wikidata.org/wiki/Q7512759","display_name":"Signal transfer function","level":4,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1080/00207721.2021.2004260","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207721.2021.2004260","pdf_url":null,"source":{"id":"https://openalex.org/S129640837","display_name":"International Journal of Systems Science","issn_l":"0020-7721","issn":["0020-7721","1464-5319"],"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 Systems Science","raw_type":"journal-article"},{"id":"pmh:oai:RePEc:taf:tsysxx:v:53:y:2022:i:7:p:1401-1415","is_oa":false,"landing_page_url":"http://hdl.handle.net/10.1080/00207721.2021.2004260","pdf_url":null,"source":{"id":"https://openalex.org/S4306401271","display_name":"RePEc: Research Papers in Economics","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I77793887","host_organization_name":"Federal Reserve Bank of St. Louis","host_organization_lineage":["https://openalex.org/I77793887"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1646046749","display_name":null,"funder_award_id":"61633014, 61922051, 61873332, U1806204, U1701264","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G3157209454","display_name":null,"funder_award_id":"2020QNQT016","funder_id":"https://openalex.org/F4320311026","funder_display_name":"Shandong University"},{"id":"https://openalex.org/G8809806507","display_name":null,"funder_award_id":"2020CXGC01208","funder_id":"https://openalex.org/F4320338074","funder_display_name":"Government of Shandong Province"}],"funders":[{"id":"https://openalex.org/F4320311026","display_name":"Shandong University","ror":"https://ror.org/0207yh398"},{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320338074","display_name":"Government of Shandong Province","ror":null}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":29,"referenced_works":["https://openalex.org/W1583323312","https://openalex.org/W1974638344","https://openalex.org/W1980568723","https://openalex.org/W1985704494","https://openalex.org/W1986260493","https://openalex.org/W1996451487","https://openalex.org/W2011192022","https://openalex.org/W2011914468","https://openalex.org/W2037349991","https://openalex.org/W2053274077","https://openalex.org/W2075672983","https://openalex.org/W2090857110","https://openalex.org/W2113657696","https://openalex.org/W2243020911","https://openalex.org/W2741883614","https://openalex.org/W2762882657","https://openalex.org/W2789241926","https://openalex.org/W2811285628","https://openalex.org/W2903678526","https://openalex.org/W2946238875","https://openalex.org/W2967002204","https://openalex.org/W3008177545","https://openalex.org/W3023318830","https://openalex.org/W3027817760","https://openalex.org/W3028708996","https://openalex.org/W3030740771","https://openalex.org/W3045978169","https://openalex.org/W3159497334","https://openalex.org/W4206422821"],"related_works":["https://openalex.org/W2005019312","https://openalex.org/W2547959172","https://openalex.org/W2018296362","https://openalex.org/W2727200542","https://openalex.org/W2002357820","https://openalex.org/W197349956","https://openalex.org/W2997206142","https://openalex.org/W2027962246","https://openalex.org/W2804494800","https://openalex.org/W2116228702"],"abstract_inverted_index":{"This":[0],"paper":[1],"studies":[2],"linear":[3],"quadratic":[4],"(LQ)":[5],"control":[6,31],"of":[7,29,32,55,63,71],"forward":[8],"and":[9,40,73],"backward":[10],"stochastic":[11,92],"difference":[12,93],"system":[13],"(FBSDS).":[14],"There":[15],"are":[16,76],"two":[17],"main":[18,83],"contributions:":[19],"first,":[20],"the":[21,27,41,48,53,61,68,90],"equivalent":[22,69],"condition":[23],"is":[24,44,58,87],"obtained":[25,77],"for":[26],"solvability":[28,72],"optimal":[30],"FBSDS":[33],"with":[34],"multi-multiplicative":[35],"noises":[36],"under":[37],"complete":[38,56],"information":[39,57],"analytic":[42],"solution":[43,75],"also":[45],"stated":[46],"by":[47],"proposed":[49],"Riccati":[50,80],"equation.":[51,81],"Second,":[52],"result":[54],"deduced":[59],"to":[60,88],"situation":[62],"incomplete":[64],"information,":[65],"that":[66],"is,":[67],"conditions":[70],"analytical":[74],"based":[78],"on":[79],"The":[82],"technique":[84],"we":[85],"use":[86],"solve":[89],"forward\u2013backward":[91],"equations":[94],"(FBSDEs)":[95],"originated":[96],"from":[97],"maximum":[98],"principle":[99],"(MP).":[100]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}