Privacy Preserving Distributed Average Consensus on Time‐Varying Directed Graphs

ABSTRACT Distributed average consensus refers to a group of agents collaboratively computing the average of their local state values through information exchange between neighboring agents. It has found extensive applications in decentralized control, information fusion, network synchronization, etc. In order to reach average consensus, most existing results rely on explicit state information exchange in local interactions. However, such information sharing unavoidably leads to private information leakage, which is problematic when involved information is sensitive and private. To address this issue, we propose a novel privacy‐preserving approach for distributed average consensus on time‐varying directed graphs. More specifically, we propose modifying the conventional surplus‐based distributed average consensus algorithm by judiciously injecting randomness into consensus parameters so that the local private values of participating agents can be obfuscated during iterative interactions. By leveraging the inherent robustness of distributed average consensus, our proposed approach is also able to ensure the accuracy of average consensus. In contrast to existing approaches such as differential privacy that compromises algorithmic accuracy or homomorphic encryption that significantly increases communication/computation overhead, our proposed dynamics enabled privacy‐preserving approach neither sacrifices average consensus accuracy nor incurs heavy communication/computation overhead. Furthermore, we rigorously characterize the convergence properties of the proposed approach under time‐varying directed graphs and provide an explicit analytical range of the consensus parameter which is sufficient to guarantee a linear convergence rate. Numerical simulations are presented to confirm the theoretical results.