A control-recoverable added-noise-based privacy scheme for LQ control in networked control systems

As networked control systems continue to evolve, ensuring the privacy of sensitive data becomes an increasingly pressing concern, especially in situations where the controller is physically separated from the plant. In this article, we propose a secure control scheme for computing linear quadratic control in a networked control system utilizing two networked controllers, a privacy encoder, and a control restorer. Specifically, the encoder generates two state signals blurred with random noise and sends them to the controllers, while the restorer reconstructs the correct control signal. The proposed design effectively preserves the privacy of the control system's state without sacrificing the control performance. We theoretically quantify the privacy-preserving performance in terms of the state estimation error of the controllers and the disclosure probability. In addition, the proposed privacy-preserving scheme is also proven to satisfy differential privacy. Moreover, we extend the proposed privacy-preserving scheme and evaluation method to cases where collusion between two controllers occurs. Finally, we verify the validity of our proposed scheme through simulations.