A Secure High-dimension Consensus Mechanism against Adversaries

This paper investigates the problem of high-dimension consensus against adversaries for multi-agent systems. Most of the existing works focus on each-dimension consensus separately. Differently, we introduce the incremental norm, i.e., the norm of local state vector's deviation for two consecutive iterations, to characterize the property of high-dimension consensus. Then, inspired by the existing two-hop-based secure one-dimension consensus, an adversary defense mechanism (ADM) against adversaries is proposed, where two-hop neighboring information is used to constrain the effect of adversaries on the performance of high-dimension consensus in a tolerable range. Specifically, if and only if the incremental norm of adversaries' state is bounded by their neighbors' maximum and minimum incremental norms, their normal neighboring agents use the transmitted state for local state update. We also show that under ADM, when adversaries do not collaborate/neighbor with each other, high-dimension consensus can be achieved and the final state is bounded by initial states of all normal agents. Finally, extensive simulations are conducted to demonstrate the effectiveness of the proposed defense mechanism.