Existing resilient consensus algorithms are mainly developed based on the mean subsequence reduced (MSR) method, which relies on the assumption that there exist at most $f$ malicious agents in the entire network or each neighborhood (i.e., $f$ -total or $f$ -local model). However, in some practical cases, it may be impossible to estimate an appropriate upper bound on the number of malicious agents. This paper proposes a novel method, called trusted-region subsequence reduction (TSR), for designing resilient consensus algorithm without the $f$ -total/local model assumption. The main idea of the TSR method is to filter out the received information beyond a dynamic trusted region, determined by the current relative positions of the neighboring trusted nodes. Based on the TSR method, we design a sampled-data resilient consensus algorithm for double-integrator multi-agent networks. A necessary and sufficient graph-theoretic condition is obtained to achieve resilient consensus. Finally, simulations are conducted to illustrate the effectiveness of the proposed algorithm and the faster convergence rate of the TSR-based algorithm than the classical MSR-based algorithm.

中文翻译：

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设计弹性共识算法的可信区域子序列约简

现有的弹性共识算法主要是基于平均均值子序列缩减（MSR）方法开发的，该方法依赖于假设最多存在 $ f $ 整个网络或每个邻域中的恶意代理（即， $ f $ -总计或 $ f $ -本地模型）。但是，在某些实际情况下，可能无法估计恶意代理数量的适当上限。本文提出了一种新的方法，称为可信赖区域子序列约简（TSR），用于设计无需协商的弹性共识算法。$ f $ -总/局部模型假设。TSR方法的主要思想是滤除超出动态受信区域的接收信息，该动态受信区域由相邻受信节点的当前相对位置确定。基于TSR方法，我们设计了一种用于双集成多主体网络的采样数据弹性共识算法。获得了必要的充分的图论条件以实现弹性共识。最后，进行仿真以说明所提出算法的有效性以及基于TSR的算法比基于经典MSR的算法更快的收敛速度。