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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2501.18853 |
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| _version_ | 1866913921731919872 |
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| author | Sun, Shuai Hu, Weikang Wang, Xu |
| author_facet | Sun, Shuai Hu, Weikang Wang, Xu |
| contents | The subspace identification method (SIM) has become a widely adopted approach for the identification of discrete-time linear time-invariant (LTI) systems. In this paper, we derive finite sample high-probability error bounds for the system matrices $A,C$, the Kalman filter gain $K$ and the estimation of system poles. Specifically, we demonstrate that, ignoring the logarithmic factors, for an $n$-dimensional LTI system with no external inputs, the estimation error of these matrices decreases at a rate of at least $ \mathcal{O}(\sqrt{1/N}) $, while the estimation error of the system poles decays at a rate of at least $ \mathcal{O}(N^{-1/2n}) $, where $ N $ represents the number of sample trajectories. Furthermore, we reveal that achieving a constant estimation error requires a super-polynomial sample size in $n/m $, where $n/m$ denotes the state-to-output dimension ratio. Finally, numerical experiments are conducted to validate the non-asymptotic results. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_18853 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Finite Sample Analysis of Subspace Identification for Stochastic Systems Sun, Shuai Hu, Weikang Wang, Xu Systems and Control The subspace identification method (SIM) has become a widely adopted approach for the identification of discrete-time linear time-invariant (LTI) systems. In this paper, we derive finite sample high-probability error bounds for the system matrices $A,C$, the Kalman filter gain $K$ and the estimation of system poles. Specifically, we demonstrate that, ignoring the logarithmic factors, for an $n$-dimensional LTI system with no external inputs, the estimation error of these matrices decreases at a rate of at least $ \mathcal{O}(\sqrt{1/N}) $, while the estimation error of the system poles decays at a rate of at least $ \mathcal{O}(N^{-1/2n}) $, where $ N $ represents the number of sample trajectories. Furthermore, we reveal that achieving a constant estimation error requires a super-polynomial sample size in $n/m $, where $n/m$ denotes the state-to-output dimension ratio. Finally, numerical experiments are conducted to validate the non-asymptotic results. |
| title | Finite Sample Analysis of Subspace Identification for Stochastic Systems |
| topic | Systems and Control |
| url | https://arxiv.org/abs/2501.18853 |