Finite Sample Analyses for Continuous-time Linear Systems: System Identification and Online Control
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| Format: | Preprint |
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2025
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| _version_ | 1866908562025873408 |
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| author | Zhou, Hongyi Li, Jingwei Zhang, Jingzhao |
| author_facet | Zhou, Hongyi Li, Jingwei Zhang, Jingzhao |
| contents | Real world evolves in continuous time but computations are done from finite samples. Therefore, we study algorithms using finite observations in continuous-time linear dynamical systems. We first study the system identification problem, and propose a first non-asymptotic error analysis with finite observations. Our algorithm identifies system parameters without needing integrated observations over certain time intervals, making it more practical for real-world applications. Further we propose a lower bound result that shows our estimator is provably optimal up to constant factors. Moreover, we apply the above algorithm to online control regret analysis for continuous-time linear system. Our system identification method allows us to explore more efficiently, enabling the swift detection of ineffective policies. We achieve a regret of $\mathcal{O}(\sqrt{T})$ over a single $T$-time horizon in a controllable system, requiring only $\mathcal{O}(T)$ observations of the system. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_22741 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Finite Sample Analyses for Continuous-time Linear Systems: System Identification and Online Control Zhou, Hongyi Li, Jingwei Zhang, Jingzhao Systems and Control Dynamical Systems Real world evolves in continuous time but computations are done from finite samples. Therefore, we study algorithms using finite observations in continuous-time linear dynamical systems. We first study the system identification problem, and propose a first non-asymptotic error analysis with finite observations. Our algorithm identifies system parameters without needing integrated observations over certain time intervals, making it more practical for real-world applications. Further we propose a lower bound result that shows our estimator is provably optimal up to constant factors. Moreover, we apply the above algorithm to online control regret analysis for continuous-time linear system. Our system identification method allows us to explore more efficiently, enabling the swift detection of ineffective policies. We achieve a regret of $\mathcal{O}(\sqrt{T})$ over a single $T$-time horizon in a controllable system, requiring only $\mathcal{O}(T)$ observations of the system. |
| title | Finite Sample Analyses for Continuous-time Linear Systems: System Identification and Online Control |
| topic | Systems and Control Dynamical Systems |
| url | https://arxiv.org/abs/2509.22741 |