Privacy preservation in matrix-scaled consensus

Matrix-scaled consensus offers a robust framework for distributed control and coordination in networks, accommodating higher-dimensional state spaces and providing flexible convergence options. However, in interconnected networks where agents regularly exchange states with their neighbors under matrix-scaled and other general consensus protocols, privacy concerns about the potential leakage of sensitive information become significant. In this work, we introduce a privacy-preserving matrix-scaled consensus framework for discrete-time connected networks. Our approach extends the state space and designs matrix-valued switching edge weights to ensure privacy. We demonstrate that the proposed strategy achieves matrix-scaled consensus, allowing for arbitrary positive definite or negative definite scaling matrices. Additionally, our choice of edge weights protects honest agents from disclosing their initial states to neighbors, thereby preserving their privacy without requiring assumptions about the number of adversaries in the network. The effectiveness of our theoretical results is validated through numerical examples, including a real-life animal interaction network.