Privacy Analysis for Quantized Networked Control Systems

Quantized signals are widely used in engineering applications. Although quantization can potentially degrade system performances, previous research has demonstrated its usage to preserve privacy of the signals that are quantized. In this paper, we investigate the privacy-preserving properties of two types of quantizers: deterministic and stochastic ones. Specifically, for deterministic quantizers, we demonstrate that an eavesdropper cannot uniquely determine the initial state of a system if the system is Schur stable. Additionally, we propose a necessary condition on the system matrix
$A$
to ensure the initial state remains private. For stochastic quantizers, we investigate their differential privacy properties and show that appropriate quantization steps can guarantee differential privacy. However, the quantization step can lead to impreciseness of the quantized signal and we therefore also examine the trade-off between differential privacy and system performance. To optimize the quantization step, we formulate a convex optimization problem, which can be solved efficiently.