{"title":"Takagi-Sugeno模糊随机系统的H∞模型约简。","authors":"Xiaojie Su, Ligang Wu, Peng Shi, Yong-Duan Song","doi":"10.1109/TSMCB.2012.2195723","DOIUrl":null,"url":null,"abstract":"<p><p>This paper is concerned with the problem of H(∞) model reduction for Takagi-Sugeno (T-S) fuzzy stochastic systems. For a given mean-square stable T-S fuzzy stochastic system, our attention is focused on the construction of a reduced-order model, which not only approximates the original system well with an H(∞) performance but also translates it into a linear lower dimensional system. Then, the model reduction is converted into a convex optimization problem by using a linearization procedure, and a projection approach is also presented, which casts the model reduction into a sequential minimization problem subject to linear matrix inequality constraints by employing the cone complementary linearization algorithm. Finally, two numerical examples are provided to illustrate the effectiveness of the proposed methods.</p>","PeriodicalId":55006,"journal":{"name":"IEEE Transactions on Systems Man and Cybernetics Part B-Cybernetics","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2012-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1109/TSMCB.2012.2195723","citationCount":"138","resultStr":"{\"title\":\"H∞ model reduction of Takagi-Sugeno fuzzy stochastic systems.\",\"authors\":\"Xiaojie Su, Ligang Wu, Peng Shi, Yong-Duan Song\",\"doi\":\"10.1109/TSMCB.2012.2195723\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p><p>This paper is concerned with the problem of H(∞) model reduction for Takagi-Sugeno (T-S) fuzzy stochastic systems. For a given mean-square stable T-S fuzzy stochastic system, our attention is focused on the construction of a reduced-order model, which not only approximates the original system well with an H(∞) performance but also translates it into a linear lower dimensional system. Then, the model reduction is converted into a convex optimization problem by using a linearization procedure, and a projection approach is also presented, which casts the model reduction into a sequential minimization problem subject to linear matrix inequality constraints by employing the cone complementary linearization algorithm. Finally, two numerical examples are provided to illustrate the effectiveness of the proposed methods.</p>\",\"PeriodicalId\":55006,\"journal\":{\"name\":\"IEEE Transactions on Systems Man and Cybernetics Part B-Cybernetics\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2012-12-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://sci-hub-pdf.com/10.1109/TSMCB.2012.2195723\",\"citationCount\":\"138\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"IEEE Transactions on Systems Man and Cybernetics Part B-Cybernetics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1109/TSMCB.2012.2195723\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"2012/5/18 0:00:00\",\"PubModel\":\"Epub\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"IEEE Transactions on Systems Man and Cybernetics Part B-Cybernetics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/TSMCB.2012.2195723","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"2012/5/18 0:00:00","PubModel":"Epub","JCR":"","JCRName":"","Score":null,"Total":0}
H∞ model reduction of Takagi-Sugeno fuzzy stochastic systems.
This paper is concerned with the problem of H(∞) model reduction for Takagi-Sugeno (T-S) fuzzy stochastic systems. For a given mean-square stable T-S fuzzy stochastic system, our attention is focused on the construction of a reduced-order model, which not only approximates the original system well with an H(∞) performance but also translates it into a linear lower dimensional system. Then, the model reduction is converted into a convex optimization problem by using a linearization procedure, and a projection approach is also presented, which casts the model reduction into a sequential minimization problem subject to linear matrix inequality constraints by employing the cone complementary linearization algorithm. Finally, two numerical examples are provided to illustrate the effectiveness of the proposed methods.