In this paper, we examine the role of stochastic quantizers for privacy preservation. We first employ a static stochastic quantizer and investigate its corresponding privacy-preserving properties. Specifically, we demonstrate that a sufficiently large quantization step guarantees $(0, \delta)$ differential privacy. Additionally, the degradation of control performance caused by quantization is evaluated as the tracking error of output regulation. These two analyses characterize the trade-off between privacy and control performance, determined by the quantization step. This insight enables us to use quantization intentionally as a means to achieve the seemingly conflicting two goals of maintaining control performance and preserving privacy at the same time; towards this end, we further investigate a dynamic stochastic quantizer. Under a stability assumption, the dynamic stochastic quantizer can enhance privacy, more than the static one, while achieving the same control performance. We further handle the unstable case by additionally applying input Gaussian noise.

翻译：本文研究了随机量化器在隐私保护中的作用。首先，我们采用静态随机量化器并探究其对应的隐私保护特性。具体而言，我们证明足够大的量化步长能够保证$(0, \delta)$-差分隐私。此外，量化对控制性能的退化通过输出调节的跟踪误差进行评估。这两项分析刻画了由量化步长决定的隐私与控制性能之间的权衡关系。这一见解使我们能够有意地将量化用作一种手段，同时实现维持控制性能与保护隐私这两个看似冲突的目标；为此，我们进一步研究了动态随机量化器。在稳定性假设下，动态随机量化器在实现相同控制性能的同时，比静态随机量化器更能增强隐私保护。针对非稳定情形，我们通过额外施加输入高斯噪声进行处理。