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arXiv · 2401.05774

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

Hiroki Sakamoto·Kazuhiro Sato
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Abstract

We present a data-driven framework for $h^{2}$-optimal model reduction for linear discrete-time systems. Our main contribution is to create optimal reduced-order models in the $h^{2}$-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 $h^{2}$ 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 $h^{2}$-norm.

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Hiroki Sakamoto, Kazuhiro Sato. 2024-01-11. Data-driven h2 model reduction for linear discrete-time systems. https://arxiv.org/abs/2401.05774

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