Towards resilient average consensus in multi-agent systems: a detection and compensation approach

Consensus is one of the fundamental distributed control technologies for collaboration in multi-agent systems such as collaborative handling in intelligent manufacturing. In this paper, we study the problem of resilient average consensus for multi-agent systems with misbehaving nodes. To protect consensus value from being influenced by misbehaving nodes, we address this problem by detecting misbehaviors, mitigating the corresponding adverse impact, and achieving the resilient average consensus. General types of misbehaviors are considered, including attacks, accidental faults, and link failures. We characterize the adverse impact of misbehaving nodes in a distributed manner via two-hop communication information and develop a deterministic detection compensation based consensus (D-DCC) algorithm with a decaying fault-tolerant error bound. Considering scenarios wherein information sets are intermittently available due to link failures, a stochastic extension named stochastic detection compensation based consensus (S-DCC) algorithm is proposed. We prove that D-DCC and S-DCC allow nodes to asymptotically achieve resilient accurate average consensus and unbiased resilient average consensus in a statistical sense, respectively. Then, the Wasserstein distance is introduced to analyze the accuracy of S-DCC. Finally, extensive simulations are conducted to verify the effectiveness of the proposed algorithms.