Frequency Shaping for Improving a Trade‐Off Between Control and Privacy Performance: Beyond Differential Privacy

ABSTRACT In privacy protection of control systems, a trade‐off between control performance and privacy level is often pointed out. Our goal in this paper is to improve this trade‐off by shaping the frequency of noise added for privacy protection when the control objective is to track a reference signal, which is taken as a piece of information whose privacy needs to be preserved. Frequency shaping of noise is achieved by passing it through a filter, thus generating noise via a dynamical system. To deal with such noise in privacy analysis, we provide a novel condition related to differential privacy, which shows that differential privacy is less effective in evaluating privacy performance in the frequency domain. To demonstrate privacy protection using frequency information, we discuss filter design in terms of the power spectrum of an estimation of private information, enabling us to obscure its power spectrum in order to preserve privacy. Furthermore, taking control performance into account, we formulate filter design to balance the trade‐off as a standard control problem. The effectiveness of the proposed method, compared with simply adding i.i.d. noise, is illustrated by numerical simulation.