{"title":"一类具有随机切换时间的最优控制问题的两种不同求解方法","authors":"Alessandra Buratto, Luca Grosset, Maddalena Muttoni","doi":"10.37394/23206.2023.22.80","DOIUrl":null,"url":null,"abstract":"In optimal control theory, strategic decision making requires the consideration of unforeseen disruptions that may arise within a predetermined time horizon. In this context, we introduce the concept of ”stochastic switching time” as a random moment in time at which a sudden, irreversible alteration takes place in the system’s dynamics or in the payoff function. To address optimal decision-making under such uncertain conditions, the literature presents two prominent methodologies: the ”backward” approach and the ”heterogeneous” approach. In this study, we offer an exposition and a comparative analysis of these two approaches. Finally, we present an illustrative example to show, in a detailed context, the advantages and disadvantages associated with these two solution strategies.","PeriodicalId":55878,"journal":{"name":"WSEAS Transactions on Mathematics","volume":"15 2 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2023-10-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Two Different Solution Techniques for an Optimal Control Problem with a Stochastic Switching Time\",\"authors\":\"Alessandra Buratto, Luca Grosset, Maddalena Muttoni\",\"doi\":\"10.37394/23206.2023.22.80\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In optimal control theory, strategic decision making requires the consideration of unforeseen disruptions that may arise within a predetermined time horizon. In this context, we introduce the concept of ”stochastic switching time” as a random moment in time at which a sudden, irreversible alteration takes place in the system’s dynamics or in the payoff function. To address optimal decision-making under such uncertain conditions, the literature presents two prominent methodologies: the ”backward” approach and the ”heterogeneous” approach. In this study, we offer an exposition and a comparative analysis of these two approaches. Finally, we present an illustrative example to show, in a detailed context, the advantages and disadvantages associated with these two solution strategies.\",\"PeriodicalId\":55878,\"journal\":{\"name\":\"WSEAS Transactions on Mathematics\",\"volume\":\"15 2 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2023-10-20\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"WSEAS Transactions on Mathematics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.37394/23206.2023.22.80\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"Mathematics\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"WSEAS Transactions on Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.37394/23206.2023.22.80","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"Mathematics","Score":null,"Total":0}
Two Different Solution Techniques for an Optimal Control Problem with a Stochastic Switching Time
In optimal control theory, strategic decision making requires the consideration of unforeseen disruptions that may arise within a predetermined time horizon. In this context, we introduce the concept of ”stochastic switching time” as a random moment in time at which a sudden, irreversible alteration takes place in the system’s dynamics or in the payoff function. To address optimal decision-making under such uncertain conditions, the literature presents two prominent methodologies: the ”backward” approach and the ”heterogeneous” approach. In this study, we offer an exposition and a comparative analysis of these two approaches. Finally, we present an illustrative example to show, in a detailed context, the advantages and disadvantages associated with these two solution strategies.
期刊介绍:
WSEAS Transactions on Mathematics publishes original research papers relating to applied and theoretical mathematics. We aim to bring important work to a wide international audience and therefore only publish papers of exceptional scientific value that advance our understanding of these particular areas. The research presented must transcend the limits of case studies, while both experimental and theoretical studies are accepted. It is a multi-disciplinary journal and therefore its content mirrors the diverse interests and approaches of scholars involved with linear algebra, numerical analysis, differential equations, statistics and related areas. We also welcome scholarly contributions from officials with government agencies, international agencies, and non-governmental organizations.