{"title":"自适应控制系统的全局分岔分析","authors":"F. Salam, S. V. van Gils, Zhang Zhi-fen","doi":"10.1109/CDC.1988.194319","DOIUrl":null,"url":null,"abstract":"The authors present a complete bifurcation analysis of a two-parameter, two-dimensional quadratic ODE (ordinary differential equation) which arises in the study of model reference adaptive control systems. The 2-D ODE exhibits saddle-node, (subcritical) Hopf, and saddle-loop bifurcations. The authors are able to describe the bifurcation diagram completely by identifying all the bifurcation curves. All but the saddle-loop bifurcation curves are explicitly characterized. The saddle-loop bifurcation curve, however, is described qualitatively, and its endpoints as well as its relative position are identified.<<ETX>>","PeriodicalId":113534,"journal":{"name":"Proceedings of the 27th IEEE Conference on Decision and Control","volume":"60 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"1988-12-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"2","resultStr":"{\"title\":\"Global bifurcation analysis of an adaptive control system\",\"authors\":\"F. Salam, S. V. van Gils, Zhang Zhi-fen\",\"doi\":\"10.1109/CDC.1988.194319\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"The authors present a complete bifurcation analysis of a two-parameter, two-dimensional quadratic ODE (ordinary differential equation) which arises in the study of model reference adaptive control systems. The 2-D ODE exhibits saddle-node, (subcritical) Hopf, and saddle-loop bifurcations. The authors are able to describe the bifurcation diagram completely by identifying all the bifurcation curves. All but the saddle-loop bifurcation curves are explicitly characterized. The saddle-loop bifurcation curve, however, is described qualitatively, and its endpoints as well as its relative position are identified.<<ETX>>\",\"PeriodicalId\":113534,\"journal\":{\"name\":\"Proceedings of the 27th IEEE Conference on Decision and Control\",\"volume\":\"60 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"1988-12-07\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"2\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Proceedings of the 27th IEEE Conference on Decision and Control\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1109/CDC.1988.194319\",\"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 27th IEEE Conference on Decision and Control","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/CDC.1988.194319","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Global bifurcation analysis of an adaptive control system
The authors present a complete bifurcation analysis of a two-parameter, two-dimensional quadratic ODE (ordinary differential equation) which arises in the study of model reference adaptive control systems. The 2-D ODE exhibits saddle-node, (subcritical) Hopf, and saddle-loop bifurcations. The authors are able to describe the bifurcation diagram completely by identifying all the bifurcation curves. All but the saddle-loop bifurcation curves are explicitly characterized. The saddle-loop bifurcation curve, however, is described qualitatively, and its endpoints as well as its relative position are identified.<>
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