A Class of Hybrid Geometric Controllers for Robust Global Asymptotic Stabilization on S1

Adeel Akhtar, Ricardo G. Sanfelice

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

3 Scopus citations


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.

Original languageEnglish (US)
Title of host publication2022 American Control Conference, ACC 2022
PublisherInstitute of Electrical and Electronics Engineers Inc.
Number of pages6
ISBN (Electronic)9781665451963
StatePublished - 2022
Event2022 American Control Conference, ACC 2022 - Atlanta, United States
Duration: Jun 8 2022Jun 10 2022

Publication series

NameProceedings of the American Control Conference
ISSN (Print)0743-1619


Conference2022 American Control Conference, ACC 2022
Country/TerritoryUnited States

Bibliographical note

Funding Information:
This research has been partially supported by the National Science Foundation under Grant no. ECS-1710621, Grant no. CNS-1544396, and Grant no. CNS-2039054, by the Air Force Office of Scientific Research under Grant no. FA9550-19-1-0053, Grant no. FA9550-19-1-0169, and Grant no. FA9550-20-1-0238, and by the Army Research Office under Grant no. W911NF-20-1-0253.

Publisher Copyright:
© 2022 American Automatic Control Council.

ASJC Scopus subject areas

  • Electrical and Electronic Engineering


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