{"title":"δ灵敏度及其在非线性扩散随机最优控制中的应用","authors":"Evangelos A. Theodorou, E. Todorov","doi":"10.1109/ACC.2013.6580486","DOIUrl":null,"url":null,"abstract":"We provide optimal control laws by using tools from stochastic calculus of variations and the mathematical concept of δ-sensitivity. The analysis relies on logarithmic transformations of the value functions and the use of linearly solvable Partial Differential Equations(PDEs). We derive the corresponding optimal control as a function of the δ-sensitivity of the logarithmic transformation of the value function for the case of nonlinear diffusion processes affine in control and noise.","PeriodicalId":145065,"journal":{"name":"2013 American Control Conference","volume":"46 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2013-06-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"The δ - sensitivity and its application to stochastic optimal control of nonlinear diffusions\",\"authors\":\"Evangelos A. Theodorou, E. Todorov\",\"doi\":\"10.1109/ACC.2013.6580486\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We provide optimal control laws by using tools from stochastic calculus of variations and the mathematical concept of δ-sensitivity. The analysis relies on logarithmic transformations of the value functions and the use of linearly solvable Partial Differential Equations(PDEs). We derive the corresponding optimal control as a function of the δ-sensitivity of the logarithmic transformation of the value function for the case of nonlinear diffusion processes affine in control and noise.\",\"PeriodicalId\":145065,\"journal\":{\"name\":\"2013 American Control Conference\",\"volume\":\"46 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2013-06-17\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"2013 American Control Conference\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1109/ACC.2013.6580486\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"2013 American Control Conference","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/ACC.2013.6580486","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
The δ - sensitivity and its application to stochastic optimal control of nonlinear diffusions
We provide optimal control laws by using tools from stochastic calculus of variations and the mathematical concept of δ-sensitivity. The analysis relies on logarithmic transformations of the value functions and the use of linearly solvable Partial Differential Equations(PDEs). We derive the corresponding optimal control as a function of the δ-sensitivity of the logarithmic transformation of the value function for the case of nonlinear diffusion processes affine in control and noise.
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