{"title":"多目标结构控制中双仿矩阵不等式问题的非线性规划方法","authors":"J. Lee","doi":"10.1109/ACC.1999.786162","DOIUrl":null,"url":null,"abstract":"Some nonlinear minimization problems are proposed for obtaining a solution of the biaffine matrix inequality (BMI) problem. An algorithm is also proposed for solving the nonlinear minimization problems. The algorithm can be easily implemented with the existing convex optimization codes. This nonlinear programming approach can be applied to all multiobjective and structured control problems such as the simultaneous stabilization by static or dynamic output feedback, the mixed H/sub 2//H/sub /spl infin// control, and the decentralized control which can be reduced to BMI problems. The effectiveness is illustrated by numerical examples.","PeriodicalId":441363,"journal":{"name":"Proceedings of the 1999 American Control Conference (Cat. No. 99CH36251)","volume":"91 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2003-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"10","resultStr":"{\"title\":\"Nonlinear programming approach to biaffine matrix inequality problems in multiobjective and structured control\",\"authors\":\"J. Lee\",\"doi\":\"10.1109/ACC.1999.786162\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Some nonlinear minimization problems are proposed for obtaining a solution of the biaffine matrix inequality (BMI) problem. An algorithm is also proposed for solving the nonlinear minimization problems. The algorithm can be easily implemented with the existing convex optimization codes. This nonlinear programming approach can be applied to all multiobjective and structured control problems such as the simultaneous stabilization by static or dynamic output feedback, the mixed H/sub 2//H/sub /spl infin// control, and the decentralized control which can be reduced to BMI problems. The effectiveness is illustrated by numerical examples.\",\"PeriodicalId\":441363,\"journal\":{\"name\":\"Proceedings of the 1999 American Control Conference (Cat. No. 99CH36251)\",\"volume\":\"91 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2003-09-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"10\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Proceedings of the 1999 American Control Conference (Cat. No. 99CH36251)\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1109/ACC.1999.786162\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Proceedings of the 1999 American Control Conference (Cat. No. 99CH36251)","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/ACC.1999.786162","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Nonlinear programming approach to biaffine matrix inequality problems in multiobjective and structured control
Some nonlinear minimization problems are proposed for obtaining a solution of the biaffine matrix inequality (BMI) problem. An algorithm is also proposed for solving the nonlinear minimization problems. The algorithm can be easily implemented with the existing convex optimization codes. This nonlinear programming approach can be applied to all multiobjective and structured control problems such as the simultaneous stabilization by static or dynamic output feedback, the mixed H/sub 2//H/sub /spl infin// control, and the decentralized control which can be reduced to BMI problems. The effectiveness is illustrated by numerical examples.
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