In this paper, we consider a multi-agent resilient consensus problem, where some of the nodes may behave maliciously. The approach is to equip all nodes with a scheme to detect neighboring nodes when they behave in an abnormal fashion. To this end, the nodes exchange not only their own states but also information regarding their neighbor nodes. Such two-hop communication has long been studied in fault-tolerant algorithms in computer science. We propose two distributed schemes for detection of malicious nodes and resilient consensus with different requirements on resources for communication and the structures of the networks. In particular, the detection schemes become effective under certain connectivity properties in the network so that the non-malicious nodes can share enough information about their neighbors. It is shown that the requirements are however less stringent than those for conventional algorithms. A numerical example is presented to demonstrate the performance of the proposed methods in wireless sensor networks.

在本文中，我们考虑了一个多代理弹性共识问题，其中一些节点可能会有恶意行为。该方法是为所有节点配备一种方案，以在相邻节点以异常方式运行时检测它们。为此，节点不仅交换自己的状态，还交换有关其邻居节点的信息。长期以来，计算机科学中的容错算法一直在研究这种两跳通信。我们提出了两种分布式方案，用于检测恶意节点和弹性共识，对通信资源和网络结构有不同的要求。特别是，检测方案在网络中的某些连接属性下变得有效，以便非恶意节点可以共享有关其邻居的足够信息。然而，结果表明，这些要求没有传统算法那么严格。给出了一个数值例子来证明所提出的方法在无线传感器网络中的性能。