Differentially Private Discrete-Time Second-Order Consensus under Directed Topologies

This paper considers the privacy protection of discrete-time second-order consensus under a directed communication topology in multi-agent systems. To protect the initial states of agents, random noise with exponentially decaying variance is added to the communication states at each iteration. We provide sufficient and necessary conditions under which consensus can be maintained, and specify the convergence rate. We analyze the level of privacy protection based on differential privacy and derive certain boundaries of privacy degrees when Laplacian or Gaussian noise is added. The definition of (b, r)-accuracy shows the lower bound 1-b of probability that the absolute position deviation from the original trajectory without noise is within r. It is used to characterize the system accuracy, and then the accuracy level is given. Simulations are conducted to validate the correctness of the obtained results.