论文标题
在谎言组上共识和同步的统一框架，承认双重视度度量
A Unified Framework for Consensus and Synchronization on Lie Groups admitting a Bi-Invariant Metric
论文作者
论文摘要
对于在欧几里得空间上演变的有限数量的代理，并通过连接的图相互链接，基于基于试剂间误差的拉普拉斯流动，可确保对一阶动力学和二阶动力学的共识或同步。当这样的试剂在圆上演变（库拉莫托振荡器）时，取决于误差间误差的正弦的流量会概括相同。在这项工作中，表明拉普拉斯流动和库拉莫托振荡器是对允许双重不变指标的谎言群体共识的更一般理论的特殊情况。这样的理论不仅可以使这些共识和同步算法的概括能够说谎群体，而且还可以深入了解抽象组理论和差异几何特性，从而确保欧几里得空间和圆圈中的收敛性。
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.
