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Towards almost global synchronization on the Stiefel manifold

Markdahl, Johan ; Thunberg, Johan LU and Gonçalves, Jorge (2018) 57th IEEE Conference on Decision and Control, CDC 2018 p.496-501
Abstract
The Kuramoto model evolves on the circle, i.e., the 1-sphere mathsf S^ 1. A graph mathcal G is referred to as mathsf S^ 1 -synchronizing if the Kuramoto model on mathcal G synchronizes almost globally. This paper generalizes the Kuramoto model and the concept of synchronizing graphs to the Stiefel manifold St (p, n). Previous work on generalizations of the Kuramoto model have largely been influenced by results and techniques that pertain to the original model. It was recently shown that all connected graphs are mathsf S^ n -synchronizing for all ngeq 2. However, that does not hold for n=1. Previous results on generalized models may thus have been overly conservative. The n-sphere is a special case of the Stiefel manifold, namely St (1,... (More)
The Kuramoto model evolves on the circle, i.e., the 1-sphere mathsf S^ 1. A graph mathcal G is referred to as mathsf S^ 1 -synchronizing if the Kuramoto model on mathcal G synchronizes almost globally. This paper generalizes the Kuramoto model and the concept of synchronizing graphs to the Stiefel manifold St (p, n). Previous work on generalizations of the Kuramoto model have largely been influenced by results and techniques that pertain to the original model. It was recently shown that all connected graphs are mathsf S^ n -synchronizing for all ngeq 2. However, that does not hold for n=1. Previous results on generalized models may thus have been overly conservative. The n-sphere is a special case of the Stiefel manifold, namely St (1, n+1). As such, it is natural to ask for the extent to which the results on mathcal S^ n can be extended to the Stiefel manifold. This paper shows that all connected graphs are St (p, n) -synchronizing provided the pair (p, n) satisfies pleqfrac 2n 3-1. (Less)
Please use this url to cite or link to this publication:
author
; and
publishing date
type
Chapter in Book/Report/Conference proceeding
publication status
published
subject
host publication
2018 IEEE Conference on Decision and Control (CDC)
pages
6 pages
publisher
IEEE - Institute of Electrical and Electronics Engineers Inc.
conference name
57th IEEE Conference on Decision and Control, CDC 2018
conference location
Miami, United States
conference dates
2018-12-17 - 2018-12-19
external identifiers
  • scopus:85062170358
ISBN
978-1-5386-1395-5
language
Unknown
LU publication?
no
id
c61742b7-b92f-4f57-bf61-a9dde87d37aa
date added to LUP
2024-09-05 14:29:47
date last changed
2025-04-04 15:06:26
@inproceedings{c61742b7-b92f-4f57-bf61-a9dde87d37aa,
  abstract     = {{The Kuramoto model evolves on the circle, i.e., the 1-sphere mathsf S^ 1. A graph mathcal G is referred to as mathsf S^ 1 -synchronizing if the Kuramoto model on mathcal G synchronizes almost globally. This paper generalizes the Kuramoto model and the concept of synchronizing graphs to the Stiefel manifold St (p, n). Previous work on generalizations of the Kuramoto model have largely been influenced by results and techniques that pertain to the original model. It was recently shown that all connected graphs are mathsf S^ n -synchronizing for all ngeq 2. However, that does not hold for n=1. Previous results on generalized models may thus have been overly conservative. The n-sphere is a special case of the Stiefel manifold, namely St (1, n+1). As such, it is natural to ask for the extent to which the results on mathcal S^ n can be extended to the Stiefel manifold. This paper shows that all connected graphs are St (p, n) -synchronizing provided the pair (p, n) satisfies pleqfrac 2n 3-1.}},
  author       = {{Markdahl, Johan and Thunberg, Johan and Gonçalves, Jorge}},
  booktitle    = {{2018 IEEE Conference on Decision and Control (CDC)}},
  isbn         = {{978-1-5386-1395-5}},
  language     = {{und}},
  pages        = {{496--501}},
  publisher    = {{IEEE - Institute of Electrical and Electronics Engineers Inc.}},
  title        = {{Towards almost global synchronization on the Stiefel manifold}},
  year         = {{2018}},
}