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- Markdahl, Johan, et al.
(författare)
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Analytical solutions to feedback systems on the special orthogonal group SO(n)
- 2013
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Ingår i: 2013 IEEE 52nd Annual Conference on Decision and Control (CDC). - : IEEE conference proceedings. - 9781467357173 ; , s. 5246-5251
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Konferensbidrag (refereegranskat)abstract
- This paper provides analytical solutions to the closed-loop kinematics of two almost globally exponentially stabilizing attitude control laws on the special orthogonal group SO(n). By studying the general case we give a uniform treatment to the cases of SO(2) and SO(3), which are the most interesting dimensions for application purposes. Working directly with rotation matrices in the case of SO(3) allows us to avoid certain complications which may arise when using local and global many-to-one parameterizations. The analytical solutions provide insight into the transient behaviour of the system and are of theoretical value since they can be used to prove almost global attractiveness of the identity matrix. The practical usefulness of analytical solutions in problems of continuous time actuation subject to piece-wise unavailable or discrete time sensing are illustrated by numerical examples.
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- Markdahl, Johan, et al.
(författare)
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Towards Almost Global Synchronization on the Stiefel Manifold
- 2018
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Ingår i: 2018 IEEE Conference on Decision and Control (CDC), Miami Beach, FL, USA, Dec. 17-19, 2018. - Miami Beach, Florida : IEEE. ; , s. 496-501
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Konferensbidrag (refereegranskat)abstract
- The Kuramoto model evolves on the circle, i.e., the 1-sphere S1. A graph G is referred to as S1 -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 Sn -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 Sn 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. © Copyright 2019 IEEE - All rights reserved.
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