{"title":"具有随机脉冲的随机微分方程的最优控制和汉密尔顿-雅各比-贝尔曼方程","authors":"Qian‐Bao Yin, Xiao‐Bao Shu, Yu Guo, Zi‐Yu Wang","doi":"10.1002/oca.3139","DOIUrl":null,"url":null,"abstract":"In this article, we study the optimal control of stochastic differential equations with random impulses. We optimize the performance index and add the influence of random impulses to the performance index with a random compensation function. Using the idea of stochastic analysis and dynamic programming principle, a new Hamilton–Jacobi–Bellman (HJB) equation is obtained, and the existence and uniqueness of its viscosity solution are proved.","PeriodicalId":501055,"journal":{"name":"Optimal Control Applications and Methods","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2024-05-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Optimal control of stochastic differential equations with random impulses and the Hamilton–Jacobi–Bellman equation\",\"authors\":\"Qian‐Bao Yin, Xiao‐Bao Shu, Yu Guo, Zi‐Yu Wang\",\"doi\":\"10.1002/oca.3139\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this article, we study the optimal control of stochastic differential equations with random impulses. We optimize the performance index and add the influence of random impulses to the performance index with a random compensation function. Using the idea of stochastic analysis and dynamic programming principle, a new Hamilton–Jacobi–Bellman (HJB) equation is obtained, and the existence and uniqueness of its viscosity solution are proved.\",\"PeriodicalId\":501055,\"journal\":{\"name\":\"Optimal Control Applications and Methods\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2024-05-03\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Optimal Control Applications and Methods\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1002/oca.3139\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Optimal Control Applications and Methods","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1002/oca.3139","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Optimal control of stochastic differential equations with random impulses and the Hamilton–Jacobi–Bellman equation
In this article, we study the optimal control of stochastic differential equations with random impulses. We optimize the performance index and add the influence of random impulses to the performance index with a random compensation function. Using the idea of stochastic analysis and dynamic programming principle, a new Hamilton–Jacobi–Bellman (HJB) equation is obtained, and the existence and uniqueness of its viscosity solution are proved.
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