Privacy Preservation for Statistical Input in Dynamical Systems

This paper addresses the challenge of privacy preservation for statistical inputs in dynamical systems. Motivated by an autonomous building application, we formulate a privacy preservation problem for statistical inputs in linear time-invariant systems. What makes this problem widely applicable is that the inputs, rather than being assumed to be deterministic, follow a probability distribution, inherently embedding privacy-sensitive information that requires protection. This formulation also presents a technical challenge as conventional differential privacy mechanisms are not directly applicable. Through rigorous analysis, we develop strategy to achieve $(0, \delta)$ differential privacy through adding noise. Finally, the effectiveness of our methods is demonstrated by revisiting the autonomous building application.