SIAM Journal on Control and Optimization, Volume 59, Issue 4, Page 2624-2644, January 2021.
In this paper we study a distributed consensus problem under the $G$-expectation. Each agent is with a first-order integrator dynamics and can only access its local information. The measurement and communication are with stochastic noises whose probability space is with uncertainties considering uncertain volatility between different agents. A distributed control protocol is designed to guarantee a consensus under mild assumptions. Consensus convergence in different senses, including $G$-mean square convergence, weak convergence in capacity, and quasi-surely convergence, is analyzed. Furthermore, with the aid of exponential inequality for $G$-martingale, the convergence rate is given without specifying the consensus gain function.

中文翻译：

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$G$-期望下带噪声的多智能体系统的分布式共识和收敛率分析

SIAM Journal on Control and Optimization，第 59 卷，第 4 期，第 2624-2644 页，2021
年1 月。在本文中，我们研究了 $G$ 期望下的分布式共识问题。每个代理都具有一阶积分器动力学，并且只能访问其本地信息。测量和通信带有随机噪声，其概率空间具有不确定性，考虑到不同代理之间的不确定波动性。分布式控制协议旨在保证在温和假设下达成共识。分析了不同意义上的共识收敛，包括$G$-均方收敛、能力弱收敛和准肯定收敛。此外，借助 $G$-martingale 的指数不等式，在不指定共识增益函数的情况下给出收敛速度。