In this work, we propose a feedback control based temporal discretization for linear quadratic optimal control problems (LQ problems) governed by controlled mean-field stochastic differential equations. We firstly decompose the original problem into two problems: a stochastic LQ problem and a deterministic one. Secondly, we discretize both LQ problems one after another relying on Riccati equations and control's feedback representations. Then, we prove the convergence rates for the proposed discretization and present an effective algorithm. Finally, a numerical example is provided to support the theoretical finding.
{"title":"Convergence rates of a discrete feedback control arising in mean-field linear quadraticoptimal control problems","authors":"Yanqing Wang","doi":"10.1360/scm-2021-0663","DOIUrl":"https://doi.org/10.1360/scm-2021-0663","url":null,"abstract":"In this work, we propose a feedback control based temporal discretization for linear quadratic optimal control problems (LQ problems) governed by controlled mean-field stochastic differential equations. We firstly decompose the original problem into two problems: a stochastic LQ problem and a deterministic one. Secondly, we discretize both LQ problems one after another relying on Riccati equations and control's feedback representations. Then, we prove the convergence rates for the proposed discretization and present an effective algorithm. Finally, a numerical example is provided to support the theoretical finding.","PeriodicalId":36277,"journal":{"name":"Scientia Sinica Mathematica","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44354696","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"On nullity and fullness of measures of noncompactness","authors":"C. Xiaoling, Cheng Lixin, He Wuyi","doi":"10.1360/ssm-2022-0137","DOIUrl":"https://doi.org/10.1360/ssm-2022-0137","url":null,"abstract":"","PeriodicalId":36277,"journal":{"name":"Scientia Sinica Mathematica","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42416996","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"量子信道的熵不确定性原理和强次可加性","authors":"L. Gao, Marius Junge, Nicholas Laracuente","doi":"10.1360/ssm-2022-0244","DOIUrl":"https://doi.org/10.1360/ssm-2022-0244","url":null,"abstract":"","PeriodicalId":36277,"journal":{"name":"Scientia Sinica Mathematica","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45554605","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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