{"title":"一个二次型调节器问题，涉及辨识问题和奇异系统","authors":"A. Favini, L. Pandolfi","doi":"10.1137/050637248","DOIUrl":null,"url":null,"abstract":"We report some results concerning the quadratic regulator problem with point penalization of the control for a class of distributed systems. This new form of the quadratic regulator problem is suggested by certain identification problems related to delay systems and by the quadratic regulator problem for singular systems. The problem studied does not admit an optimal control. Hence we study the properties of the value function and we characterize the set of initial conditions which admit an optimal control. Finally, we show that it is always possible to construct minimizing sequences which are \"robust\" under perturbations on the initial conditions (and reference signals)","PeriodicalId":347035,"journal":{"name":"2006 14th Mediterranean Conference on Control and Automation","volume":"45 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2006-06-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"4","resultStr":"{\"title\":\"A quadratic regulator problem related to identification problems and singular systems\",\"authors\":\"A. Favini, L. Pandolfi\",\"doi\":\"10.1137/050637248\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We report some results concerning the quadratic regulator problem with point penalization of the control for a class of distributed systems. This new form of the quadratic regulator problem is suggested by certain identification problems related to delay systems and by the quadratic regulator problem for singular systems. The problem studied does not admit an optimal control. Hence we study the properties of the value function and we characterize the set of initial conditions which admit an optimal control. Finally, we show that it is always possible to construct minimizing sequences which are \\\"robust\\\" under perturbations on the initial conditions (and reference signals)\",\"PeriodicalId\":347035,\"journal\":{\"name\":\"2006 14th Mediterranean Conference on Control and Automation\",\"volume\":\"45 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2006-06-28\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"4\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"2006 14th Mediterranean Conference on Control and Automation\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1137/050637248\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"2006 14th Mediterranean Conference on Control and Automation","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1137/050637248","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
A quadratic regulator problem related to identification problems and singular systems
We report some results concerning the quadratic regulator problem with point penalization of the control for a class of distributed systems. This new form of the quadratic regulator problem is suggested by certain identification problems related to delay systems and by the quadratic regulator problem for singular systems. The problem studied does not admit an optimal control. Hence we study the properties of the value function and we characterize the set of initial conditions which admit an optimal control. Finally, we show that it is always possible to construct minimizing sequences which are "robust" under perturbations on the initial conditions (and reference signals)
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