  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 paper, 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.
