Trustworthy Distributed Average Consensus Based on Locally Assessed Trust Evaluations

This article proposes a distributed algorithm for average consensus in a multiagent system under a fixed bidirectional communication topology, in the presence of untrustworthy (malicious) agents (nodes) that may try to influence the average consensus outcome by manipulating their updates. The proposed algorithm converges asymptotically to the average of the initial values of the trustworthy (nonmalicious) nodes, which we refer to as the trustworthy average, as long as the underlying topology that describes the information exchange among the trustworthy nodes is connected. We first present a distributed iterative algorithm that assumes that each node receives (at each iteration or periodically) side information about the trustworthiness of the other nodes, and it uses such trust assessments to determine whether or not to incorporate messages received from its neighbors, as well as to make proper adjustments in its calculation depending on whether a previously trustworthy neighbor becomes untrustworthy or vice-versa. We show that, as long as the trust assessments for each trustworthy node eventually reflect correctly the status (trustworthy or untrustworthy) of its neighboring nodes, the algorithm guarantees asymptotic convergence to the trustworthy average. We subsequently discuss how the proposed algorithm can be enhanced with functionality that enables each node to obtain trust assessments about its neighbors by utilizing information that it receives from its two-hop neighbors at infrequent, perhaps randomly chosen, time instants.