Linear consensus protocol is an iterative distributed algorithm with asymptotic convergence guarantees. This paper develops and analyzes an algorithm for agents running linear consensus iterations to detect convergence to consensus within a specified error tolerance in a distributed manner. The distributed stopping criterion allows for time-varying bounded delays in information transmission and reception between agents. The algorithm relies on distributively determining the maximum and minimum values held by the agents. This paper further develops an algorithm for average consensus that utilizes a distributive stopping criterion, based on maximum and minimum consensus, where no centralized coordination is needed on how each agent weights its neighbor's values. Here, the doubly stochastic assumption on the weight matrix is relaxed and only column stochasticity is needed. The effectiveness of the algorithms is demonstrated by simulations and a comparison with prior work in the literature. Moreover, the demonstration of the proposed algorithms on an experimental test bed of Raspberry-Pi agents communicating wirelessly validates its applicability and utility.

中文翻译：

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存在延误的分布式停止标准

线性共识协议是一种具有渐近收敛性保证的迭代分布式算法。本文开发并分析了一种算法，该算法用于运行线性共识迭代的代理以分布式方式检测在指定的容错范围内共识的收敛性。分布式停止准则允许在代理之间进行信息传输和接收时随时间变化的有限延迟。该算法依赖于分布式确定代理所拥有的最大值和最小值。本文进一步开发了一种基于平均和最大共识的平均共识算法，该算法基于最大和最小共识，使用了分布式停止准则，其中无需集中协调每个代理如何加权其邻居的值。这里，权矩阵上的双重随机假设被放宽，只需要列随机性。通过仿真以及与文献中先前工作的比较证明了算法的有效性。此外，在无线通信的Raspberry-Pi代理的实验测试床上对提出的算法进行的演示验证了其适用性和实用性。