Byzantine Attack Resilient Bounded Consensus

Average consensus is a cornerstone of distributed systems, facilitating essential functionalities such as distributed information fusion, decision-making, and decentralized control. However, achieving the exact average consensus is challenging when partial nodes are compromised and act as Byzantine attackers by transmitting malicious messages using judiciously crafted patterns. Existing resilient consensus results can only guarantee that the consensus value under Byzantine attacks remains within the range defined by the maximum and minimum initial state values of all legitimate nodes. In addition, the consensus value is highly uncertain when attack strategies change. In this letter, we propose a new resilient consensus algorithm that ensures the consensus value falls within a much tighter bound. The bound contains the exact average consensus value and is solely determined by the initial states of legitimate nodes, regardless of the attack strategies employed by the Byzantine attackers. More interestingly, we demonstrate that the bound is the tightest achievable under our resilient consensus algorithm when the number of Byzantine attackers reaches the maximum threshold our algorithm can handle. Numerical simulations are given to validate the theoretical results.