Cohesion in networks during transitions from one consensus value to another, i.e., the ability of agents to respond in a similar manner during the transition, can be as important as achieving the new consensus value. Existing decentralized network control strategies mainly concern with the convergence speed to the final consensus value. However, even with increased convergence speed, the level of cohesion loss during transitions can be large. This loss of cohesion during transition (and tracking of varying consensus values) can be alleviated using a recently developed delayed self reinforcement (DSR) approach. However, the current DSR-based approach assumes ideal conditions with agents having instant access to neighbor information—without network delays arising during sensing or communication between neighbors, as well as computation of control actions of each agent, which can cause instability. The main contributions of this article are to use the Rouchè’s theorem to 1) prove the stability of the DSR approach if the network delay is not too large; and 2) compute an estimate of the acceptable network delay margin (DM) for stability. Additionally, a simulation example is used to illustrate the estimation approach for network DMs with DSR, and show that cohesion is maintained with DSR even with network delays when compared to the case without DSR.

中文翻译：

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网络延迟下高阶代理过渡期间的分散凝聚响应


从一种共识值过渡到另一种共识值期间网络的凝聚力，即代理在过渡期间以类似方式响应的能力，可能与实现新的共识值一样重要。现有的去中心化网络控制策略主要关注最终共识值的收敛速度。然而，即使收敛速度提高，过渡期间的内聚损失水平也可能很大。使用最近开发的延迟自我强化（DSR）方法可以缓解过渡期间（以及跟踪不同共识值）凝聚力的损失。然而，当前基于 DSR 的方法假设代理能够即时访问邻居信息的理想条件，而不会在邻居之间的感知或通信过程中出现网络延迟，也不会在计算每个代理的控制操作时出现网络延迟，这可能会导致不稳定。本文的主要贡献是利用Rouchè定理来1）证明DSR方法在网络延迟不太大的情况下的稳定性； 2) 计算可接受的网络延迟裕度 (DM) 的稳定性估计值。此外，还使用一个仿真示例来说明具有 DSR 的网络 DM 的估计方法，并表明与没有 DSR 的情况相比，即使存在网络延迟，DSR 也能保持内聚性。