Can Inherent Communication Noise Guarantee Privacy in Distributed Cooperative Control ?

TL;DR

This work addresses privacy in distributed cooperative control for multi-agent systems by showing that inherent, state-dependent communication noise can provide bounded $({\epsilon},{\delta})$-differential privacy without injecting additional privacy noise. It develops a finite-horizon LQR framework where agents exchange noisy state information and uses martingale-based convergence analysis to prove that the tracking errors converge to a finite random limit in both mean square and almost surely. The privacy analysis leverages instantaneous privacy budgets and adaptive sequential composition to establish bounded differential privacy over an infinite horizon, given appropriate decay of the coupling sequence $c(t)$. A numerical example with three agents demonstrates formation convergence and concrete privacy budgets (e.g., $\epsilon\approx 29.96$, $\delta\approx 0.0017$), validating the approach's practicality. Overall, the paper offers a privacy-preserving alternative to artificially injected noise in distributed control, with potential impact on robotic formations and cyber-physical systems operating over noisy networks.

Abstract

This paper investigates privacy-preserving distributed cooperative control for multi-agent systems within the framework of differential privacy. In cooperative control, communication noise is inevitable and is usually regarded as a disturbance that impairs coordination. This work revisits such noise as a potential privacy-enhancing factor. A linear quadratic regulator (LQR)-based framework is proposed for agents communicating over noisy channels, \textcolor{black}{where the noise variance depends on the relative state differences between neighbouring agents.} The resulting controller achieves formation while protecting the reference signals from inference attacks. It is analytically proven that the inherent communication noise can guarantee bounded $(ε,δ)$-differential privacy without adding dedicated privacy noise, while the \textcolor{black}{system cooperative tracking error} remains bounded and convergent in both the mean-square and almost-sure sense.

Figures (2)

• Figure 1: Evolution of Relative States and Privacy Budget
• Figure 2: Trajectories of Robots

Theorems & Definitions (9)

• Lemma 1
• Definition 1: Adjacent Relation
• Definition 2
• Lemma 2
• Lemma 3
• Theorem 1
• Remark 1
• Theorem 2
• Remark 2