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Electrical Engineering and Systems Science > Systems and Control

arXiv:2209.00345 (eess)
[Submitted on 1 Sep 2022 (v1), last revised 2 Sep 2022 (this version, v2)]

Title:A Unified Framework for Consensus and Synchronization on Lie Groups admitting a Bi-Invariant Metric

Authors:Rama Seshan Chandrasekharan, Ravi N Banavar, Arun D Mahindrakar
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Abstract:For a finite number of agents evolving on a Euclidean space and linked to each other by a connected graph, the Laplacian flow that is based on the inter-agent errors, ensures consensus or synchronization for both first and second-order dynamics. When such agents evolve on a circle (the Kuramoto oscillator), the flow that depends on the sinusoid of the inter-agent error angles generalizes the same. In this work, it is shown that the Laplacian flow and the Kuramoto oscillator are special cases of a more general theory of consensus on Lie groups that admit bi-invariant metrics. Such a theory not only enables generalization of these consensus and synchronization algorithms to Lie groups but also provide insight on to the abstract group theoretic and differential geometric properties that ensures convergence in Euclidean space and the circle.
Subjects: Systems and Control (eess.SY)
Cite as: arXiv:2209.00345 [eess.SY]
  (or arXiv:2209.00345v2 [eess.SY] for this version)
  https://doi.org/10.48550/arXiv.2209.00345

Submission history

From: Ravi Banavar [view email]
[v1] Thu, 1 Sep 2022 10:26:47 UTC (860 KB)
[v2] Fri, 2 Sep 2022 16:11:27 UTC (860 KB)
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