Initial State Privacy of Nonlinear Systems on Riemannian Manifolds

In this paper, we investigate initial state privacy protection for discrete-time nonlinear closed systems. By capturing Riemannian geometric structures inherent in such privacy challenges, we refine the concept of differential privacy through the introduction of an initial state adjacency set based on Riemannian distances. A new differential privacy condition is formulated using incremental output boundedness, enabling the design of time-varying Laplacian noise to achieve specified privacy guarantees. The proposed framework extends beyond initial state protection to also cover system parameter privacy, which is demonstrated as a special application.