{"title":"多时间尺度奇异摄动系统次优调节器的并行设计","authors":"Y. Wang, P. Frank","doi":"10.1109/CDC.1991.261315","DOIUrl":null,"url":null,"abstract":"The problem for near optimal control of linear systems with multiple-time-scale singular perturbations is studied by a descriptor variable approach. The near optimum regulator problem with multiple-time-scale singular perturbations is decomposed into a number of N+1 subregulator problems. The solutions are mutually independent, and are standard solutions of Riccati equations without parasitic parameters. The algorithm for parallel solutions of these subregulator problems is presented. A hierarchical combination of these suboptimal regulators leads to the near-optimal feedback controller. The spectral factorization of the linear quadratic regulator (LQR) shows that for small and unknown singularly perturbed parameters, the near-optimal controller will preserve the robustness gain and phase margin as established in the optimal LQR.<<ETX>>","PeriodicalId":344553,"journal":{"name":"[1991] Proceedings of the 30th IEEE Conference on Decision and Control","volume":" 666","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"1991-12-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"2","resultStr":"{\"title\":\"Parallel design of suboptimal regulators for singularly perturbed systems with multiple-time scales\",\"authors\":\"Y. Wang, P. Frank\",\"doi\":\"10.1109/CDC.1991.261315\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"The problem for near optimal control of linear systems with multiple-time-scale singular perturbations is studied by a descriptor variable approach. The near optimum regulator problem with multiple-time-scale singular perturbations is decomposed into a number of N+1 subregulator problems. The solutions are mutually independent, and are standard solutions of Riccati equations without parasitic parameters. The algorithm for parallel solutions of these subregulator problems is presented. A hierarchical combination of these suboptimal regulators leads to the near-optimal feedback controller. The spectral factorization of the linear quadratic regulator (LQR) shows that for small and unknown singularly perturbed parameters, the near-optimal controller will preserve the robustness gain and phase margin as established in the optimal LQR.<<ETX>>\",\"PeriodicalId\":344553,\"journal\":{\"name\":\"[1991] Proceedings of the 30th IEEE Conference on Decision and Control\",\"volume\":\" 666\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"1991-12-11\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"2\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"[1991] Proceedings of the 30th IEEE Conference on Decision and Control\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1109/CDC.1991.261315\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"[1991] Proceedings of the 30th IEEE Conference on Decision and Control","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/CDC.1991.261315","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Parallel design of suboptimal regulators for singularly perturbed systems with multiple-time scales
The problem for near optimal control of linear systems with multiple-time-scale singular perturbations is studied by a descriptor variable approach. The near optimum regulator problem with multiple-time-scale singular perturbations is decomposed into a number of N+1 subregulator problems. The solutions are mutually independent, and are standard solutions of Riccati equations without parasitic parameters. The algorithm for parallel solutions of these subregulator problems is presented. A hierarchical combination of these suboptimal regulators leads to the near-optimal feedback controller. The spectral factorization of the linear quadratic regulator (LQR) shows that for small and unknown singularly perturbed parameters, the near-optimal controller will preserve the robustness gain and phase margin as established in the optimal LQR.<>