Optimal Privacy-Aware Co-Design of Quantizer and Controller in Networked Control Systems

TL;DR

This paper develops a method to design optimal privacy-preserving quantizers and controllers in networked control systems, balancing control performance and privacy leakage.

Contribution

It introduces a stochastic control framework with mutual information regularization and derives structural properties of the optimal solution.

Findings

Optimal controller is deterministic.

Quantizer regulates adversary's belief to enhance privacy.

Numerical experiments validate the approach on building control systems.

Abstract

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.