{"title":"圆柱体传热lq -最优控制问题的积分-微分方法","authors":"A. Gavrikov, G. Kostin","doi":"10.1109/MMAR.2018.8486076","DOIUrl":null,"url":null,"abstract":"Optimal boundary control problems with linear-quadratic cost functions are considered for heat transfer processes in a cylindrical body. The method of integro-differential relations is used to reduce the original PDE model to a finite-dimensional controlled system. Three types of linear-quadratic cost functions are studied: the first includes control functions and terminal temperature distribution, the second additionally takes into account the heat flux at the terminal time instant and the third contains a measure of approximation error. Numerical examples are given and discussed.","PeriodicalId":201658,"journal":{"name":"2018 23rd International Conference on Methods & Models in Automation & Robotics (MMAR)","volume":"14 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2018-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"3","resultStr":"{\"title\":\"An Integro-Differential Approach to LQ-Optimal Control Problems for Heat Transfer in a Cylindrical Body\",\"authors\":\"A. Gavrikov, G. Kostin\",\"doi\":\"10.1109/MMAR.2018.8486076\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Optimal boundary control problems with linear-quadratic cost functions are considered for heat transfer processes in a cylindrical body. The method of integro-differential relations is used to reduce the original PDE model to a finite-dimensional controlled system. Three types of linear-quadratic cost functions are studied: the first includes control functions and terminal temperature distribution, the second additionally takes into account the heat flux at the terminal time instant and the third contains a measure of approximation error. Numerical examples are given and discussed.\",\"PeriodicalId\":201658,\"journal\":{\"name\":\"2018 23rd International Conference on Methods & Models in Automation & Robotics (MMAR)\",\"volume\":\"14 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2018-08-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"3\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"2018 23rd International Conference on Methods & Models in Automation & Robotics (MMAR)\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1109/MMAR.2018.8486076\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"2018 23rd International Conference on Methods & Models in Automation & Robotics (MMAR)","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/MMAR.2018.8486076","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
An Integro-Differential Approach to LQ-Optimal Control Problems for Heat Transfer in a Cylindrical Body
Optimal boundary control problems with linear-quadratic cost functions are considered for heat transfer processes in a cylindrical body. The method of integro-differential relations is used to reduce the original PDE model to a finite-dimensional controlled system. Three types of linear-quadratic cost functions are studied: the first includes control functions and terminal temperature distribution, the second additionally takes into account the heat flux at the terminal time instant and the third contains a measure of approximation error. Numerical examples are given and discussed.
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