{"title":"A Class of Hybrid Geometric Controllers for Robust Global Asymptotic Stabilization on S1","authors":"Adeel Akhtar, R. Sanfelice","doi":"10.23919/ACC53348.2022.9867666","DOIUrl":null,"url":null,"abstract":"This paper proposes a hybrid geometric control scheme for the classical problem of globally stabilizing a pointmass system on a unit circle, as it is impossible to design a smooth globally asymptotically stable controller for this problem. Unlike most existing solutions that rely on coordinates and rely on a particular controller construction, our proposed solution is coordinate free (or geometric) and belongs to a class of controllers that we also characterize. Specifically, we propose a geometric hybrid controller that uses a local geometric controller (from the said class) and an open-loop geometric controller. The system achieves global asymptotic stability when each controller from the local geometric class is combined with the geometric open-loop controller using a hybrid systems framework. Moreover, the hybrid geometric controller guarantees robust asymptotic stability. Simulations validate the stability properties of the proposed hybrid geometric controller.","PeriodicalId":366299,"journal":{"name":"2022 American Control Conference (ACC)","volume":"43 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2022-06-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"2","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"2022 American Control Conference (ACC)","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.23919/ACC53348.2022.9867666","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 2
Abstract
This paper proposes a hybrid geometric control scheme for the classical problem of globally stabilizing a pointmass system on a unit circle, as it is impossible to design a smooth globally asymptotically stable controller for this problem. Unlike most existing solutions that rely on coordinates and rely on a particular controller construction, our proposed solution is coordinate free (or geometric) and belongs to a class of controllers that we also characterize. Specifically, we propose a geometric hybrid controller that uses a local geometric controller (from the said class) and an open-loop geometric controller. The system achieves global asymptotic stability when each controller from the local geometric class is combined with the geometric open-loop controller using a hybrid systems framework. Moreover, the hybrid geometric controller guarantees robust asymptotic stability. Simulations validate the stability properties of the proposed hybrid geometric controller.