Differentially Private LQ Control

TL;DR

This paper introduces a differentially private multi-agent linear-quadratic control framework that balances privacy protection with system performance, providing control-theoretic guidelines and demonstrating effectiveness through numerical results.

Contribution

It develops a novel privacy-preserving control framework for multi-agent systems using differential privacy, with analysis and guidelines for balancing privacy and performance.

Findings

System performance remains acceptable under strict privacy.

Control-theoretic analysis quantifies privacy impact.

Guidelines for calibrating privacy parameters are provided.

Abstract

As multi-agent systems proliferate and share more user data, new approaches are needed to protect sensitive data while still enabling system operation. To address this need, this paper presents a private multi-agent LQ control framework. Agents' state trajectories can be sensitive and we therefore protect them using differential privacy. We quantify the impact of privacy along three dimensions: the amount of information shared under privacy, the control-theoretic cost of privacy, and the tradeoffs between privacy and performance. These analyses are done in conventional control-theoretic terms, which we use to develop guidelines for calibrating privacy as a function of system parameters. Numerical results indicate that system performance remains within desirable ranges, even under strict privacy requirements.