Privacy-preserving average consensus via matrix-weighted inter-agent coupling

Abstract

Achieving average consensus without disclosing the initial agents’ state is critical for secure multi-agent coordination. This paper proposes a novel privacy-preserving average consensus algorithm via a matrix-weighted inter-agent coupling mechanism. Specifically, the algorithm first lifts each agent state to a higher-dimensional space, then employs a dedicatedly designed matrix-valued state coupling mechanism to conceal the initial agents’ state while guaranteeing that the multi-agent network achieves average consensus. The convergence analysis is transformed into the average consensus problem on matrix-weighted switching networks with low-rank, positive semi-definite coupling matrices. We show that the average consensus can be guaranteed and discuss its performance in the presence of honest-but-curious agents and external eavesdroppers. The algorithm, involving only basic matrix operations, is computationally more efficient than cryptography-based approaches and can be implemented without relying on a centralized third party. Numerical results are provided to illustrate the effectiveness of the algorithm.