Data-driven h2 model reduction for linear discrete-time systems

We present a data-driven framework for h2-optimal model reduction for linear discrete-time systems. Our main contribution is to create optimal reduced-order models in the h2-norm sense directly from the measurement data alone, without using the information about the original system. In particular, we focus on the fact that the gradients of the h2 model reduction problem are expressed using the discrete-time Lyapunov equation and the discrete-time Sylvester equation, and derive the data-driven gradients. The proposed algorithm uses the output of an existing MOR as the initial point, and convergence to a stationary point is guaranteed under certain assumptions. In numerical experiments, we demonstrate that, for a modeling task in neuroscience, our method constructs a reduced-order model that outperforms DMDc in terms of the h2-norm.