Differentially Private Consensus Control for Discrete-time Multi-Agent Systems: Encoding-Decoding Schemes

This paper is concerned with the differentially private consensus control (DPCC) problem for linear discrete-time multi-agent systems (MASs) under dynamic encoding-decoding schemes (EDSs), where the agents' initial states are the sensitive data to be protected from potential eavesdroppers. The EDS is deployed on each agent to compress the data before transmission so as to better utilize the limited network bandwidth. Differential privacy, as a performance metric, is introduced to evaluate the level of privacy, and an EDS-based DPCC scheme is proposed to ensure the ultimate mean-square consensus with preserved differential privacy. A set of criteria is first established for the EDS-embedded DPCC problem in terms of the performance of consensus, the size of transmitted data, and the level of privacy. Subsequently, the co-design issue is discussed for the EDS, the differentially private mechanism, and the consensus controller. Finally, the effectiveness of the developed algorithm is illustrated via numerical simulations.