{"title":"无限阶双曲型系统的初始状态最优控制","authors":"A. Kowalewski","doi":"10.1109/MMAR.2010.5587221","DOIUrl":null,"url":null,"abstract":"Various optimization problems associated with the optimal control of second order time delay hyperbolic systems have been studied in [5], [6], [7], [8], [9] and [10] respectively. In this paper, we consider an optimal control problem for a linear infinite order hyperbolic system. One from the initial conditions is given by control function. Sufficient conditions for the existence of a unique solution of such hyperbolic equations with the Dirichlet boundary conditions are presented. The performance functional has the quadratic form. The time horizon T is fixed. Finally, we impose some constraints on the control. Making use of the Lions scheme ([11]), necessary and sufficient conditions of optimality for the Dirichlet problem with the quadratic performance functional and constrained control are derived.","PeriodicalId":336219,"journal":{"name":"2010 15th International Conference on Methods and Models in Automation and Robotics","volume":"18 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2010-09-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"2","resultStr":"{\"title\":\"Optimal control via initial state of an infinite order hyperbolic system\",\"authors\":\"A. Kowalewski\",\"doi\":\"10.1109/MMAR.2010.5587221\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Various optimization problems associated with the optimal control of second order time delay hyperbolic systems have been studied in [5], [6], [7], [8], [9] and [10] respectively. In this paper, we consider an optimal control problem for a linear infinite order hyperbolic system. One from the initial conditions is given by control function. Sufficient conditions for the existence of a unique solution of such hyperbolic equations with the Dirichlet boundary conditions are presented. The performance functional has the quadratic form. The time horizon T is fixed. Finally, we impose some constraints on the control. Making use of the Lions scheme ([11]), necessary and sufficient conditions of optimality for the Dirichlet problem with the quadratic performance functional and constrained control are derived.\",\"PeriodicalId\":336219,\"journal\":{\"name\":\"2010 15th International Conference on Methods and Models in Automation and Robotics\",\"volume\":\"18 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2010-09-27\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"2\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"2010 15th International Conference on Methods and Models in Automation and Robotics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1109/MMAR.2010.5587221\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"2010 15th International Conference on Methods and Models in Automation and Robotics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/MMAR.2010.5587221","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Optimal control via initial state of an infinite order hyperbolic system
Various optimization problems associated with the optimal control of second order time delay hyperbolic systems have been studied in [5], [6], [7], [8], [9] and [10] respectively. In this paper, we consider an optimal control problem for a linear infinite order hyperbolic system. One from the initial conditions is given by control function. Sufficient conditions for the existence of a unique solution of such hyperbolic equations with the Dirichlet boundary conditions are presented. The performance functional has the quadratic form. The time horizon T is fixed. Finally, we impose some constraints on the control. Making use of the Lions scheme ([11]), necessary and sufficient conditions of optimality for the Dirichlet problem with the quadratic performance functional and constrained control are derived.