Paper Info
Title
Towards Almost Global Synchronization on the Stiefel Manifold
Abstract
The Kuramoto model evolves on the circle, i.e., the 1-sphere S <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sup> . A graph G is referred to as S <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sup> -synchronizing if the Kuramoto model on 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 S <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</sup> -synchronizing for all n ≥ 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 S <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</sup> 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 p ≤ [2n/3]-1.
Year
DOI
Venue
2018
10.1109/CDC.2018.8619593
2018 IEEE Conference on Decision and Control (CDC)
Keywords
Field
DocType
connected graphs,Kuramoto model,synchronizing graphs,Stiefel manifold,almost global synchronization
Graph,Synchronization,Mathematical optimization,Combinatorics,Generalization,Computer science,Synchronizing,Stiefel manifold,Kuramoto model
Conference
ISSN
ISBN
Citations 
0743-1546
978-1-5386-1396-2
1
PageRank 
References 
Authors
0.40
12
3
Name
Order
Citations
PageRank
johan markdahl1297.43
Johan Thunberg213819.15
Goncalves, J.340442.24