Data informativity for stabilization of discrete-time infinite-dimensional systems
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866914165330804736 |
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| author | Wakaiki, Masashi |
| author_facet | Wakaiki, Masashi |
| contents | This paper develops a data-driven framework for stabilization of discrete-time infinite-dimensional systems. We investigate informativity for stabilization, defined as the existence of a feedback gain that stabilizes all systems compatible with the available input-state data. Assuming that infinite-length data are Bessel sequences, we first establish a sufficient condition for data informativity in the noise-free case. We next show that this sufficient condition is also necessary under a mild data assumption when the input space is one-dimensional. Furthermore, if the state sequence forms a frame, then the sufficient condition can be extended to the case of noisy data. Finally, when the unstable part of the true system is known to be finite-dimensional, we derive a necessary and sufficient condition for data informativity of finite-length data. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_16008 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Data informativity for stabilization of discrete-time infinite-dimensional systems Wakaiki, Masashi Optimization and Control This paper develops a data-driven framework for stabilization of discrete-time infinite-dimensional systems. We investigate informativity for stabilization, defined as the existence of a feedback gain that stabilizes all systems compatible with the available input-state data. Assuming that infinite-length data are Bessel sequences, we first establish a sufficient condition for data informativity in the noise-free case. We next show that this sufficient condition is also necessary under a mild data assumption when the input space is one-dimensional. Furthermore, if the state sequence forms a frame, then the sufficient condition can be extended to the case of noisy data. Finally, when the unstable part of the true system is known to be finite-dimensional, we derive a necessary and sufficient condition for data informativity of finite-length data. |
| title | Data informativity for stabilization of discrete-time infinite-dimensional systems |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2511.16008 |