Trust is the Cure to Distributed Consensus with Adversaries

Distributed consensus is a prototypical distributed optimization and decision making problem in social, economic and engineering networked systems. In collaborative applications investigating the effects of adversaries is a critical problem. In this paper we investigate distributed consensus problems in the presence of adversaries. We combine key ideas from distributed consensus in computer science on one hand and in control systems on the other. The main idea is to detect Byzantine adversaries in a network of collaborating agents who have as goal reaching consensus, and exclude them from the consensus process and dynamics. We describe a novel trust-aware consensus algorithm that integrates the trust evaluation mechanism into the distributed consensus algorithm and propose various local decision rules based on local evidence. To further enhance the robustness of trust evaluation itself, we also introduce a trust propagation scheme in order to take into account evidences of other nodes in the network. The resulting algorithm is flexible and extensible, and can incorporate more complex designs of decision rules and trust models. To demonstrate the power of our trust-aware algorithm, we provide new theoretical security performance results in terms of miss detection and false alarm rates for regular and general trust graphs. We demonstrate through simulations that the new trust-aware consensus algorithm can effectively detect Byzantine adversaries and can exclude them from consensus iterations even in sparse networks with connectivity less than 2f+1, where f is the number of adversaries.