As a quantitative criterion for privacy of “mechanisms” in the form of data-generating processes, the concept of differential privacy was first proposed in computer science and has later been applied to linear dynamical systems. However, differential privacy has not been studied in depth together with other properties of dynamical systems, and it has not been fully utilized for controller design. In this article, first we clarify that a classical concept in systems and control, input observability (sometimes referred to as left invertibility) has a strong connection with differential privacy. In particular, we show that the Gaussian mechanism can be made highly differentially private by adding small noise, if the corresponding system is less input observable. Next, enabled by our new insight into privacy, we develop a method to design dynamic controllers for the classic tracking control problem while addressing privacy concerns. We call the obtained controller through our design method the privacy-preserving controller. The usage of such controllers is further illustrated by an example of tracking the prescribed power supply in a dc microgrid installed with smart meters while keeping the electricity consumers' tracking errors private.

中文翻译：

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隐私保护动态控制器的设计


作为数据生成过程形式的“机制”隐私的量化标准，差分隐私的概念首先在计算机科学中提出，后来被应用于线性动力系统。然而，差分隐私尚未与动力系统的其他特性一起得到深入研究，并且尚未充分用于控制器设计。在本文中，我们首先澄清系统和控制中的一个经典概念，输入可观察性（有时称为左可逆性）与差分隐私有很强的联系。特别是，我们表明，如果相应的系统输入可观察性较小，则可以通过添加小噪声来使高斯机制具有高度差分隐私性。接下来，借助我们对隐私的新见解，我们开发了一种方法来设计动态控制器，以解决经典跟踪控制问题，同时解决隐私问题。我们将通过我们的设计方法获得的控制器称为隐私保护控制器。通过跟踪安装有智能电表的直流微电网中的规定电源，同时保持电力消费者的跟踪误差不公开的示例，进一步说明了此类控制器的使用。