{"title":"一维LQG寻的解析解","authors":"M. Lefebvre, F. Zitouni","doi":"10.1080/21642583.2013.878886","DOIUrl":null,"url":null,"abstract":"The problem of optimally controlling one-dimensional diffusion processes until they leave a given interval is considered. By linearizing the Riccati differential equation satisfied by the derivative of the value function in the so-called linear quadratic Gaussian homing problem, we are able to obtain an exact expression for the solution to the general problem. Particular problems are solved explicitly.","PeriodicalId":22127,"journal":{"name":"Systems Science & Control Engineering: An Open Access Journal","volume":"25 1","pages":"41 - 47"},"PeriodicalIF":0.0000,"publicationDate":"2014-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"17","resultStr":"{\"title\":\"Analytical solutions to LQG homing problems in one dimension\",\"authors\":\"M. Lefebvre, F. Zitouni\",\"doi\":\"10.1080/21642583.2013.878886\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"The problem of optimally controlling one-dimensional diffusion processes until they leave a given interval is considered. By linearizing the Riccati differential equation satisfied by the derivative of the value function in the so-called linear quadratic Gaussian homing problem, we are able to obtain an exact expression for the solution to the general problem. Particular problems are solved explicitly.\",\"PeriodicalId\":22127,\"journal\":{\"name\":\"Systems Science & Control Engineering: An Open Access Journal\",\"volume\":\"25 1\",\"pages\":\"41 - 47\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2014-12-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"17\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Systems Science & Control Engineering: An Open Access Journal\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1080/21642583.2013.878886\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Systems Science & Control Engineering: An Open Access Journal","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1080/21642583.2013.878886","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Analytical solutions to LQG homing problems in one dimension
The problem of optimally controlling one-dimensional diffusion processes until they leave a given interval is considered. By linearizing the Riccati differential equation satisfied by the derivative of the value function in the so-called linear quadratic Gaussian homing problem, we are able to obtain an exact expression for the solution to the general problem. Particular problems are solved explicitly.
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