Computationally Light Privacy Preservation of Matrix-Weighted Average Consensus

Abstract

Multiagent consensus algorithms have emerged as foundational tools across a spectrum of applications, and matrix-weighted consensus ones are capable of characterizing cross-dimensional interdependence. Yet, their potential is often shadowed by a pressing concern: the privacy of agents' initial values, which frequently represent sensitive data or proprietary information. A computationally light privacy-preserving mechanism for matrix-weighted average consensus (MAC) algorithms is proposed in response to the concern of agents' privacy. In the mechanism, agents' states are first perturbed and then multiplied by the matrix weights before being sent to their neighbors. Both the perturbation and the matrix weight are neighbor-dependent, i.e., they may be selected to be different for different neighbors, and they can be selected independently to mask the true state of an agent. The proposed mechanism can simultaneously guarantee the privacy of initial values and accurate average consensus. The additional computational burden that an agent bears is only the addition of vectors in the same dimension as its state compared to the original MAC algorithm. Through practical case studies with a peer-to-peer transactive energy system, we demonstrate the tangible implications of safeguarding initial value privacy with the proposed mechanism.