Data-driven h2 model reduction for linear discrete-time systems
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866908557163626496 |
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| author | Sakamoto, Hiroki Sato, Kazuhiro |
| author_facet | Sakamoto, Hiroki Sato, Kazuhiro |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2401_05774 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Data-driven h2 model reduction for linear discrete-time systems Sakamoto, Hiroki Sato, Kazuhiro Optimization and Control 93C05, 93C15, 78M34, 78M50, 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. |
| title | Data-driven h2 model reduction for linear discrete-time systems |
| topic | Optimization and Control 93C05, 93C15, 78M34, 78M50, |
| url | https://arxiv.org/abs/2401.05774 |