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Control Contraction Metrics on Submanifolds

Wu, Dongjun LU ; Yi, Bowen and Manchester, Ian (2024) p.3735-3740
Abstract
In this paper, we extend the control contraction metrics (CCM) approach, which was originally proposed for the universal tracking control of nonlinear systems, to those that evolves on Lie groups. Our idea is to view the manifold as a constrained set that is embedded in Euclidean space, and then propose the sufficient conditions for the existence of a CCM and the associated controller design. Notably, we demonstrate that the search for CCM on Lie groups can be reformulated as convex conditions. The results extend the applicability of the CCM approach and provide a framework for analyzing the behavior of control systems with Lie group structures.
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author
; and
organization
publishing date
type
Chapter in Book/Report/Conference proceeding
publication status
published
subject
host publication
Proceedings of the IEEE Conference on Decision and Control
pages
3735 - 3740
publisher
IEEE - Institute of Electrical and Electronics Engineers Inc.
external identifiers
  • scopus:86000557254
ISBN
979-835031633-9
DOI
10.1109/CDC56724.2024.10886040
project
Scalable Control of Interconnected Systems
language
English
LU publication?
yes
id
907a107c-0587-41b6-9329-0dd09de47912
date added to LUP
2025-01-08 16:41:45
date last changed
2025-06-03 09:25:59
@inproceedings{907a107c-0587-41b6-9329-0dd09de47912,
  abstract     = {{In this paper, we extend the control contraction metrics (CCM) approach, which was originally proposed for the universal tracking control of nonlinear systems, to those that evolves on Lie groups. Our idea is to view the manifold as a constrained set that is embedded in Euclidean space, and then propose the sufficient conditions for the existence of a CCM and the associated controller design. Notably, we demonstrate that the search for CCM on Lie groups can be reformulated as convex conditions. The results extend the applicability of the CCM approach and provide a framework for analyzing the behavior of control systems with Lie group structures.}},
  author       = {{Wu, Dongjun and Yi, Bowen and Manchester, Ian}},
  booktitle    = {{Proceedings of the IEEE Conference on Decision and Control}},
  isbn         = {{979-835031633-9}},
  language     = {{eng}},
  pages        = {{3735--3740}},
  publisher    = {{IEEE - Institute of Electrical and Electronics Engineers Inc.}},
  title        = {{Control Contraction Metrics on Submanifolds}},
  url          = {{http://dx.doi.org/10.1109/CDC56724.2024.10886040}},
  doi          = {{10.1109/CDC56724.2024.10886040}},
  year         = {{2024}},
}