发表机构
Linköping University（林雪平大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
针对持续链路扰动下标准随机逼近迭代无法精确平均的问题，本文提出基于去中心化梯度的锚定机制，证明其几乎必然收敛到精确初始平均值，并给出统一框架与设计原则。
AI 中文摘要
我们研究了在持续链路级扰动下的分布式平均一致性（distributed average consensus）问题，该扰动被建模为具有一致有界条件二阶矩的鞅差序列（martingale difference sequence）。在此类扰动下，基于随机逼近（stochastic approximation）的标准线性迭代，采用递减步长，会使网络收敛到某个无偏随机变量的一致值，但其方差不消失，而非精确的初始平均值。为理解并解决这一局限，我们基于去中心化梯度下降（decentralized gradient descent）公式，开发了一种基于锚定（anchoring）的机制，并研究了加入一个衰减锚定项的效果，该锚定项持续将每个智能体状态拉向其初始值。这一视角为状态锚定如何抵消扰动累积提供了直观解释。在标准可和性条件下，我们证明了所提算法几乎必然实现精确平均一致性。此外，该去中心化梯度视角为若干相关方法提供了统一框架，并为在持续扰动下实现精确平均一致性提供了可解释的设计原则。
英文摘要
We study the distributed average consensus problem under persistent link-level disturbances modeled as a martingale difference sequence with uniformly bounded conditional second moments. Under such disturbances, the standard stochastic-approximation-based linear iteration with diminishing stepsizes drives the network to consensus on an unbiased random variable with non-vanishing variance instead of the exact initial average. To understand and resolve this limitation, we develop an anchoring-based mechanism derived from a decentralized gradient descent formulation and study the effect of incorporating a decaying anchoring term that continuously pulls each agent state toward its initial value. This perspective provides an intuitive interpretation of how state anchoring counteracts disturbance accumulation. Under standard summability conditions, we prove that the resulting algorithm achieves exact average consensus almost surely. Furthermore, this decentralized gradient perspective offers a unifying framework for several related methods and an interpretable design principle for exact average consensus under persistent disturbances.
Comments8 pages, 2 figures. Accepted to the 2026 IEEE 65th Conference on Decision and Control (CDC 2026)
