System Design Approach for Control of Differentially Private Dynamical Systems

This paper introduces a novel approach to concurrently design dynamic controllers and correlated differential privacy noise in dynamic control systems. An increase in privacy noise increases the system's privacy but adversely affects the system's performance. Our approach optimizes the noise distribution while shaping closed-loop system dynamics such that the privacy noise has the least impact on system performance and the most effect on system privacy. We further add privacy noise to both control input and system output to privatize the system's state for an adversary with access to both communication channels and direct output measurements. The study also suggests tailored privacy bounds for different states, providing a comprehensive framework for jointly optimizing system performance and privacy in the context of differential privacy.