Hybrid Geometric Controllers for Fully-Actuated Left-invariant Systems on Matrix Lie Groups

Adeel Akhtar; Ricardo G. Sanfelice

doi:10.1109/CDC51059.2022.9992659

Hybrid Geometric Controllers for Fully-Actuated Left-invariant Systems on Matrix Lie Groups

Adeel Akhtar, Ricardo G. Sanfelice

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Abstract

This paper proposes a hybrid geometric control scheme for a system defined on a matrix Lie group in the form of a left-invariant vector field. Our solution to the point stabilization problem is coordinate free (or geometric). Specifically, we propose a hybrid geometric controller that uses a controller from a local class of geometric controllers and an open-loop geometric controller. Our method guarantees that the given point in the manifold is robustly globally asymptotically stable for the closed-loop system when each controller from the local geometric class is combined with the geometric open-loop controller using a hybrid systems framework.

Original language	English (US)
Title of host publication	2022 IEEE 61st Conference on Decision and Control, CDC 2022
Publisher	Institute of Electrical and Electronics Engineers Inc.
Pages	1855-1860
Number of pages	6
ISBN (Electronic)	9781665467612
DOIs	https://doi.org/10.1109/CDC51059.2022.9992659
State	Published - 2022
Externally published	Yes
Event	61st IEEE Conference on Decision and Control, CDC 2022 - Cancun, Mexico Duration: Dec 6 2022 → Dec 9 2022

Publication series

Name	Proceedings of the IEEE Conference on Decision and Control
Volume	2022-December
ISSN (Print)	0743-1546
ISSN (Electronic)	2576-2370

Conference

Conference	61st IEEE Conference on Decision and Control, CDC 2022
Country/Territory	Mexico
City	Cancun
Period	12/6/22 → 12/9/22

All Science Journal Classification (ASJC) codes

Control and Systems Engineering
Modeling and Simulation
Control and Optimization

Access to Document

10.1109/CDC51059.2022.9992659

Cite this

Akhtar, A., & Sanfelice, R. G. (2022). Hybrid Geometric Controllers for Fully-Actuated Left-invariant Systems on Matrix Lie Groups. In 2022 IEEE 61st Conference on Decision and Control, CDC 2022 (pp. 1855-1860). (Proceedings of the IEEE Conference on Decision and Control; Vol. 2022-December). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/CDC51059.2022.9992659

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title = "Hybrid Geometric Controllers for Fully-Actuated Left-invariant Systems on Matrix Lie Groups",

abstract = "This paper proposes a hybrid geometric control scheme for a system defined on a matrix Lie group in the form of a left-invariant vector field. Our solution to the point stabilization problem is coordinate free (or geometric). Specifically, we propose a hybrid geometric controller that uses a controller from a local class of geometric controllers and an open-loop geometric controller. Our method guarantees that the given point in the manifold is robustly globally asymptotically stable for the closed-loop system when each controller from the local geometric class is combined with the geometric open-loop controller using a hybrid systems framework.",

author = "Adeel Akhtar and Sanfelice, {Ricardo G.}",

note = "Publisher Copyright: {\textcopyright} 2022 IEEE.; 61st IEEE Conference on Decision and Control, CDC 2022 ; Conference date: 06-12-2022 Through 09-12-2022",

year = "2022",

doi = "10.1109/CDC51059.2022.9992659",

language = "English (US)",

series = "Proceedings of the IEEE Conference on Decision and Control",

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Akhtar, A & Sanfelice, RG 2022, Hybrid Geometric Controllers for Fully-Actuated Left-invariant Systems on Matrix Lie Groups. in 2022 IEEE 61st Conference on Decision and Control, CDC 2022. Proceedings of the IEEE Conference on Decision and Control, vol. 2022-December, Institute of Electrical and Electronics Engineers Inc., pp. 1855-1860, 61st IEEE Conference on Decision and Control, CDC 2022, Cancun, Mexico, 12/6/22. https://doi.org/10.1109/CDC51059.2022.9992659

Hybrid Geometric Controllers for Fully-Actuated Left-invariant Systems on Matrix Lie Groups. / Akhtar, Adeel; Sanfelice, Ricardo G.
2022 IEEE 61st Conference on Decision and Control, CDC 2022. Institute of Electrical and Electronics Engineers Inc., 2022. p. 1855-1860 (Proceedings of the IEEE Conference on Decision and Control; Vol. 2022-December).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

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AU - Sanfelice, Ricardo G.

PY - 2022

Y1 - 2022

N2 - This paper proposes a hybrid geometric control scheme for a system defined on a matrix Lie group in the form of a left-invariant vector field. Our solution to the point stabilization problem is coordinate free (or geometric). Specifically, we propose a hybrid geometric controller that uses a controller from a local class of geometric controllers and an open-loop geometric controller. Our method guarantees that the given point in the manifold is robustly globally asymptotically stable for the closed-loop system when each controller from the local geometric class is combined with the geometric open-loop controller using a hybrid systems framework.

AB - This paper proposes a hybrid geometric control scheme for a system defined on a matrix Lie group in the form of a left-invariant vector field. Our solution to the point stabilization problem is coordinate free (or geometric). Specifically, we propose a hybrid geometric controller that uses a controller from a local class of geometric controllers and an open-loop geometric controller. Our method guarantees that the given point in the manifold is robustly globally asymptotically stable for the closed-loop system when each controller from the local geometric class is combined with the geometric open-loop controller using a hybrid systems framework.

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T3 - Proceedings of the IEEE Conference on Decision and Control

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BT - 2022 IEEE 61st Conference on Decision and Control, CDC 2022

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Y2 - 6 December 2022 through 9 December 2022

ER -

Hybrid Geometric Controllers for Fully-Actuated Left-invariant Systems on Matrix Lie Groups

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All Science Journal Classification (ASJC) codes

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