{"title":"一类二阶非线性系统的稳定性定理及其在机器人中的应用","authors":"M. Grabbe, D. Dawson","doi":"10.1109/SECON.1992.202383","DOIUrl":null,"url":null,"abstract":"Optimal control theory is used to generate a feedback control which stabilizes a class of second-order nonlinear systems. Specifically, the Hamilton-Jacobi-Bellman (HJB) equation of dynamic programming is used to show that the control is the solution to a quadratic optimal control problem in which the second-order system serves as a dynamic constraint. The stability result follows from the fact that the solution to the HJB equation serves as a Lyapunov function for the given system. An application of this result to the trajectory tracking of a robot manipulator is given.<<ETX>>","PeriodicalId":230446,"journal":{"name":"Proceedings IEEE Southeastcon '92","volume":"5 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"1992-04-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"A stability theorem for a class of second order nonlinear systems with an application to robotics\",\"authors\":\"M. Grabbe, D. Dawson\",\"doi\":\"10.1109/SECON.1992.202383\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Optimal control theory is used to generate a feedback control which stabilizes a class of second-order nonlinear systems. Specifically, the Hamilton-Jacobi-Bellman (HJB) equation of dynamic programming is used to show that the control is the solution to a quadratic optimal control problem in which the second-order system serves as a dynamic constraint. The stability result follows from the fact that the solution to the HJB equation serves as a Lyapunov function for the given system. An application of this result to the trajectory tracking of a robot manipulator is given.<<ETX>>\",\"PeriodicalId\":230446,\"journal\":{\"name\":\"Proceedings IEEE Southeastcon '92\",\"volume\":\"5 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"1992-04-12\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Proceedings IEEE Southeastcon '92\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1109/SECON.1992.202383\",\"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 IEEE Southeastcon '92","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/SECON.1992.202383","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
A stability theorem for a class of second order nonlinear systems with an application to robotics
Optimal control theory is used to generate a feedback control which stabilizes a class of second-order nonlinear systems. Specifically, the Hamilton-Jacobi-Bellman (HJB) equation of dynamic programming is used to show that the control is the solution to a quadratic optimal control problem in which the second-order system serves as a dynamic constraint. The stability result follows from the fact that the solution to the HJB equation serves as a Lyapunov function for the given system. An application of this result to the trajectory tracking of a robot manipulator is given.<>
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