Differential privacy optimal control with asymmetric information structure

Abstract

A linear‐quadratic optimal control is investigated in this article under the differential privacy (DP) philosophy to trade off the performance and privacy of sensitive information, where the two controllers have asymmetric information structure and some prescribed signal needs to be tracked. Note that the system output and tracking signal are always sensitive and easy to be filched by adversaries; thus the DP methodology is explored to protect them. Under DP Gaussian mechanism, the optimal linear controllers are first studied for finite‐horizon and infinite‐horizon problems. Then, the bounds of mean‐square error of steady‐state Kalman filter estimator is provided, and the DP parameter design will be guided that characterizes the privacy of sensitive information. As the DP Gaussian noise will degrade the controlled performance, the degraded performance is quantitatively calculated. Finally, a numerical example is given that shows the efficiency of obtained results.