{"title":"Approximability of Sliding Modes and Regularization","authors":"L. Levaggi, S. Villa","doi":"10.1109/VSS.2006.1644512","DOIUrl":null,"url":null,"abstract":"Approximability of sliding motions for control systems governed by nonlinear finite-dimensional differential equations is considered. This regularity property is shown to be equivalent to Tikhonov well-posedness of a related minimisation problem in the context of relaxed controls. This allows us to give a general approximability result, which in the autonomous case has an easy to verify geometrical formulation. In the second part of the paper, we consider non-approximable sliding mode control systems. In the flavour of regularization of ill-posed problems, we propose a method of selection of well-behaved approximating trajectories converging to a prescribed ideal sliding","PeriodicalId":146618,"journal":{"name":"International Workshop on Variable Structure Systems, 2006. VSS'06.","volume":"39 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2006-06-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"International Workshop on Variable Structure Systems, 2006. VSS'06.","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/VSS.2006.1644512","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
Approximability of sliding motions for control systems governed by nonlinear finite-dimensional differential equations is considered. This regularity property is shown to be equivalent to Tikhonov well-posedness of a related minimisation problem in the context of relaxed controls. This allows us to give a general approximability result, which in the autonomous case has an easy to verify geometrical formulation. In the second part of the paper, we consider non-approximable sliding mode control systems. In the flavour of regularization of ill-posed problems, we propose a method of selection of well-behaved approximating trajectories converging to a prescribed ideal sliding