Gossip over holonomic graphs
Gossip over holonomic graphs
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DOI：
10.1016/j.automatica.2021.110088
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发表时间：
2021-02
期刊：
影响因子：
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通讯作者：
Xudong Chen;M. Belabbas;Ji Liu
中科院分区：
文献类型：
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作者：
Xudong Chen;M. Belabbas;Ji Liu
八卦过程是多代理系统中的迭代过程，其中每次迭代时只有两个相邻代理进行通信并更新其状态。按照惯例，相邻条件由无向图描述。在本文中，我们考虑一个通用更新规则，每个代理对其及其邻居的当前状态进行任意加权平均值。一般来说，八卦过程的极限（如果它收敛）取决于八卦对的迭代顺序。本文的主要贡献是为八卦过程的收敛提供了一个与迭代顺序无关的充分必要条件。这一结果依赖于为通信图引入局部随机矩阵完整概念的新概念。我们还提供了图上完整随机矩阵的极限和空间的完整表征。
A gossip process is an iterative process in a multi-agent system where only two neighboring agents communicate at each iteration and update their states. The neighboring condition is by convention described by an undirected graph. In this paper, we consider a general update rule whereby each agent takes an arbitrary weighted average of its and its neighbor’s current states. In general, the limit of the gossip process (if it converges) depends on the order of iterations of the gossiping pairs. The main contribution of the paper is to provide a necessary and sufficient condition for convergence of the gossip process that is independent of the order of iterations. This result relies on the introduction of the novel notion of holonomy of local stochastic matrices for the communication graph. We also provide complete characterizations of the limit and the space of holonomic stochastic matrices over the graph.