{"title":"具有跳变马尔可夫扰动系统的最优控制的存在性","authors":"Robert M. Goor","doi":"10.1137/0314057","DOIUrl":null,"url":null,"abstract":"We consider stochastic optimal control problems of Mayer type with dynamics in the form of a system of ordinary differential equations perturbed by a countable state Markov process, and we prove the existence of an optimal control in the class of non-anticipative functions. The proof takes the same approach as the \"direct\" method of the calculus of variations, used extensively in deterministic problems, but substitutes probabilistic concepts where necessary.","PeriodicalId":164707,"journal":{"name":"1975 IEEE Conference on Decision and Control including the 14th Symposium on Adaptive Processes","volume":"40 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"1975-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"3","resultStr":"{\"title\":\"Existence of an optimal control for systems with jump Markov disturbances\",\"authors\":\"Robert M. Goor\",\"doi\":\"10.1137/0314057\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We consider stochastic optimal control problems of Mayer type with dynamics in the form of a system of ordinary differential equations perturbed by a countable state Markov process, and we prove the existence of an optimal control in the class of non-anticipative functions. The proof takes the same approach as the \\\"direct\\\" method of the calculus of variations, used extensively in deterministic problems, but substitutes probabilistic concepts where necessary.\",\"PeriodicalId\":164707,\"journal\":{\"name\":\"1975 IEEE Conference on Decision and Control including the 14th Symposium on Adaptive Processes\",\"volume\":\"40 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"1975-12-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"3\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"1975 IEEE Conference on Decision and Control including the 14th Symposium on Adaptive Processes\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1137/0314057\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"1975 IEEE Conference on Decision and Control including the 14th Symposium on Adaptive Processes","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1137/0314057","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Existence of an optimal control for systems with jump Markov disturbances
We consider stochastic optimal control problems of Mayer type with dynamics in the form of a system of ordinary differential equations perturbed by a countable state Markov process, and we prove the existence of an optimal control in the class of non-anticipative functions. The proof takes the same approach as the "direct" method of the calculus of variations, used extensively in deterministic problems, but substitutes probabilistic concepts where necessary.
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