Differentially Private Consensus of Two-Time-Scale Multiagent Systems

This article investigates the differentially private leader-following consensus control (DPLFCC) problem for multiagent systems (MASs) operating on two-time scales. A new co-design framework with a private preserving scheme and a consensus controller is constructed by building a unique time-scale-dependent Lyapunov function. To achieve the ultimate mean-square leader-following consensus while maintaining differential privacy, the proposed strategy establishes a new distributed consensus controller with noise control for each follower. The initial state of the follower can be made more private by adjusting the noise control gain. It should be pointed out that controller-solving criteria and privacy level performances are designed depending on the time-scale parameter, thereby eliminating the numerical stiffness caused by the two-time-scale property. Furthermore, the results are extended to the leader's privacy-preserving situation. Finally, the effectiveness of the developed algorithm is illustrated by numerical simulation examples.