{"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}
引用次数: 1
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.<>
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