Optimal Privacy-Aware Co-Design of Quantizer and Controller in Networked Control Systems
This work addresses privacy protection in networked control systems, which is crucial for applications like smart infrastructure, but it is incremental as it builds on existing methods for privacy-aware control.
The paper tackles the problem of designing a quantizer and controller for networked control systems to protect private inputs from adversaries, achieving optimal privacy by solving a stochastic control problem with mutual information regularization and validating the approach on a building control system.
This paper investigates the optimal privacy-aware networked control problem, in which the dynamical system affected by a private input process sends its measurement to a remote controller after stochastic quantization. An adversary seeks to infer private system inputs from quantization results and control outputs. The optimal privacy-aware quantizer and controller are obtained by solving a stochastic control problem with mutual information regularization, where the mutual information measures the privacy leakage through the quantizer and controller. We first derive the coupled Bellman equations for the optimal quantizer and controller using the dynamic programming decomposition method. We then analyze the structural properties of the solution, showing that the optimal controller is deterministic, while the optimal quantizer regulates the adversary's belief in a closed-loop manner to enhance privacy. To enable numerical optimization, the quantizer and controller are jointly parameterized and then updated via policy gradient methods, and a binary classification approach is used to approximate privacy leakage. Finally, we validate the effectiveness of the proposed approach through numerical experiments on a building control system.