Distributed Finite-Horizon Optimal Control for Consensus with Differential Privacy Guarantees

Abstract: This paper addresses the problem of privacy-preserving consensus control for multi-agent systems (MAS) using differential privacy. We propose a novel distributed finite-horizon linear quadratic regulator (LQR) framework, in which agents share individual state information while preserving the confidentiality of their local pairwise weight matrices, which are considered sensitive data in MAS. Protecting these matrices effectively safeguards each agent's private cost function and control preferences. Our solution injects consensus error-dependent Laplace noise into the communicated state information and employs a carefully designed time-dependent scaling factor in the local cost functions. {This approach guarantees bounded consensus and achieves rigorous $\epsilon$-differential privacy for the weight matrices without relying on specific noise distribution assumptions.} Additionally, we analytically characterize the trade-off between consensus accuracy and privacy level, offering clear guidelines on how to enhance consensus performance through appropriate scaling of the LQR weight matrices and the privacy budget.