Differentially Private Consensus for Multi-Agent Systems

This paper considers the distributed consensus problems for first-order multi-agent systems subject to differentially private requirements, where we protect the privacy of the agents' initial states against an adversary that has access to all the messages. Compared with the existing results, we propose a stochastic approximation-type protocol to deal with the injected noises. Furthermore, the 6-differential privacy and convergence property of the proposed algorithm are established. The privacy of each agent's initial states is protected by the designed protocol. Meanwhile, the agent's state converges in mean square to a common random variable, whose expectation is right the average of the initial states of the whole system. Finally, the effectiveness of the proposed method is demonstrated by numerical simulations.