Preserving Data-Privacy Cooperative Control of Discrete-Time Multi-Agent Systems

With the rapid advancements of communication technology, distributed cooperative control has emerged as a promising approach, enabling participants to perform control based on their neighbouring agents, thereby facilitating a faster response and more flexibility. However, the privacy concerns must be addressed not only on the external adversaries but also on the internal adversaries, to encourage the participant to join this cooperative network. In contrast to existing literature, our study considers the scenario where participating agents are unaware of whether their neighbouring nodes inject noises, leading them to directly use the received data in control. We first design the noise injection scheme to ensure the mean-square consensus while preserving privacy in discrete-time multi-agent systems (MASs) and then derive the upper and lower bounds of the convergence rate. After that, we study the covariance matrix of the maximum likelihood estimate on the initial state of other agents based on the internal adversary's local information. The feasibility of (ϵ,δ)-differential privacy is characterized. Simulations of a practical cooperative adaptive cruise control illustrate the effectiveness of the Privacy-Preserving Cooperative Control (PPCC).