存在丢包通信链路时的分布式一致与协调算法——第二部分：遍历性系数分析方法
Distributed Algorithms for Consensus and Coordination in the Presence of Packet-Dropping Communication Links - Part II: Coefficients of Ergodicity Analysis Approach
AI总结：
本文通过将鲁棒化共识方案的集体动力学重写为有限非齐次马尔可夫链，并利用遍历性系数方法证明其收敛性，从而解决丢包链路下的分布式平均计算问题。
摘要：
在这篇由两部分组成的论文中，我们考虑多组件系统，其中每个组件可以迭代地与其邻域中的其他组件交换信息，以分布式方式计算组件初始值的平均值或其他感兴趣的量（即这些初始值的某个函数）。特别地，我们研究了一种用于计算节点初始值平均值的迭代算法。在该算法中，每个组件维护两组变量，这些变量通过两个相同的线性迭代进行更新。每个节点可以渐近地将其维护的两个变量的比值作为节点初始值的平均值。在本文的第一部分，我们展示了如何增强两组变量的更新规则，使得算法能够容忍通信链路独立地、以及在不同传输时间之间独立地丢包。在这第二部分中，通过重写两个迭代的集体动力学，我们证明所得系统在数学上等价于一个有限非齐次马尔可夫链，其转移矩阵在每一步取有限个值之一。然后，通过使用遍历性系数方法（一种常用于马尔可夫链收敛分析的方法），我们证明了鲁棒化共识方案的收敛性。该分析表明，在更一般的条件下也应存在类似的收敛性。
英文摘要：
In this two-part paper, we consider multicomponent systems in which each component can iteratively exchange information with other components in its neighborhood in order to compute, in a distributed fashion, the average of the components' initial values or some other quantity of interest (i.e., some function of these initial values). In particular, we study an iterative algorithm for computing the average of the initial values of the nodes. In this algorithm, each component maintains two sets of variables that are updated via two identical linear iterations. The average of the initial values of the nodes can be asymptotically computed by each node as the ratio of two of the variables it maintains. In the first part of this paper, we show how the update rules for the two sets of variables can be enhanced so that the algorithm becomes tolerant to communication links that may drop packets, independently among them and independently between different transmission times. In this second part, by rewriting the collective dynamics of both iterations, we show that the resulting system is mathematically equivalent to a finite inhomogenous Markov chain whose transition matrix takes one of finitely many values at each step. Then, by using e a coefficients of ergodicity approach, a method commonly used for convergence analysis of Markov chains, we prove convergence of the robustified consensus scheme. The analysis suggests that similar convergence should hold under more general conditions as well.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
