{"title":"一类反馈控制系统混沌行为的概率表征","authors":"K. Loparo, X. Feng","doi":"10.1109/CDC.1990.203819","DOIUrl":null,"url":null,"abstract":"The authors investigate a family of two-dimensional nonlinear feedback systems which do not satisfy the Lipschitz continuity condition and exhibit chaotic behavior. The geometric Poincare map. is determined analytically and a bifurcation study in terms of two canonical parameters and the associated asymptotic behavior of the systems are presented. Ergodic theory of one-dimensional dynamic systems is used to derive a probabilistic description of the chaotic motions inside the chaotic attractor. It is shown that the chaotic motion is isometric to an experiment of randomly tossing an uneven die.<<ETX>>","PeriodicalId":287089,"journal":{"name":"29th IEEE Conference on Decision and Control","volume":"25 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"1990-12-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Probabilistic characterization of chaotic behavior in a family of feedback control systems\",\"authors\":\"K. Loparo, X. Feng\",\"doi\":\"10.1109/CDC.1990.203819\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"The authors investigate a family of two-dimensional nonlinear feedback systems which do not satisfy the Lipschitz continuity condition and exhibit chaotic behavior. The geometric Poincare map. is determined analytically and a bifurcation study in terms of two canonical parameters and the associated asymptotic behavior of the systems are presented. Ergodic theory of one-dimensional dynamic systems is used to derive a probabilistic description of the chaotic motions inside the chaotic attractor. It is shown that the chaotic motion is isometric to an experiment of randomly tossing an uneven die.<<ETX>>\",\"PeriodicalId\":287089,\"journal\":{\"name\":\"29th IEEE Conference on Decision and Control\",\"volume\":\"25 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"1990-12-05\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"29th IEEE Conference on Decision and Control\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1109/CDC.1990.203819\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"29th IEEE Conference on Decision and Control","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/CDC.1990.203819","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Probabilistic characterization of chaotic behavior in a family of feedback control systems
The authors investigate a family of two-dimensional nonlinear feedback systems which do not satisfy the Lipschitz continuity condition and exhibit chaotic behavior. The geometric Poincare map. is determined analytically and a bifurcation study in terms of two canonical parameters and the associated asymptotic behavior of the systems are presented. Ergodic theory of one-dimensional dynamic systems is used to derive a probabilistic description of the chaotic motions inside the chaotic attractor. It is shown that the chaotic motion is isometric to an experiment of randomly tossing an uneven die.<>
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