Privacy-preserving average consensus for multi-agent systems based on edge decomposition

This paper studies the problem of privacy preservation in achieving the average consensus of dynamic Multi-Agent Systems (MAS). Average consensus performs an essential role in dynamic MAS to promote collaboration, coordinate decision-making, resolve conflicts, and enhance system reliability. The process of achieving average consensus requires the information exchange between agents, which raises concerns about sensitive data leakage. To address this issue, we propose a novel algorithm that combines state decomposition with edge characteristics in network topology to protect the critical data during the average consensus process. Specifically, the original state of each agent is decomposed into |N_i| + 1 substates, where |N_i|represents the number of neighboring nodes. For each agent, the public substate performs the function of the original state to participate in computation and interaction between other agents, while the private parts only interact with the first one of the same agent and keep invisible to other agents. Unlike other approaches that focus solely on the privacy preservation of agents’ initial state information, this paper extends to dynamic state of agents at every moment. Next, rigorous proofs of the accuracy in average consensus are provided. Furthermore, it is shown that privacy can be protected by employing our algorithm if agent i has at least one neighbor who is not an honest-but-curious agent. As for external eavesdroppers, a sufficient condition is presented that the state information is not estimated with any guaranteed accuracy. Finally, numerical simulations are presented to verify the effectiveness of our approach.