Snapshot data-driven covariance steering for linear dynamical systems

This paper addresses a covariance steering problem for linear dynamical systems. A key feature of the problem is that the system model is unknown, and only a few snapshot data points on state variations are available. To address this challenge, the problem is decomposed into two parts: data-driven modeling based on snapshot data and a covariance steering problem toward the desired distribution using the estimated model. For the data-driven modeling problem, we propose a solution method based on the Schrödinger bridge formulation, as studied in prior work. For the model-based covariance steering problem, we develop a gradient-based algorithm in which the gradient is computed using two solutions of Lyapunov equations. Finally, we present a numerical simulation to demonstrate the effectiveness of the proposed approach.