Non-Asymptotic Bounds for Closed-Loop Identification of Unstable Nonlinear Stochastic Systems
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866908156858204160 |
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| author | Siriya, Seth Zhu, Jingge Nešić, Dragan Pu, Ye |
| author_facet | Siriya, Seth Zhu, Jingge Nešić, Dragan Pu, Ye |
| contents | We consider the problem of least squares parameter estimation from single-trajectory data for discrete-time, unstable, closed-loop nonlinear stochastic systems, with linearly parameterised uncertainty. Assuming a region of the state space produces informative data, and the system is sub-exponentially unstable, we establish non-asymptotic guarantees on the estimation error at times where the state trajectory evolves in this region. If the whole state space is informative, high probability guarantees on the error hold for all times. Examples are provided where our results are useful for analysis, but existing results are not. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_04157 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Non-Asymptotic Bounds for Closed-Loop Identification of Unstable Nonlinear Stochastic Systems Siriya, Seth Zhu, Jingge Nešić, Dragan Pu, Ye Systems and Control Machine Learning Optimization and Control We consider the problem of least squares parameter estimation from single-trajectory data for discrete-time, unstable, closed-loop nonlinear stochastic systems, with linearly parameterised uncertainty. Assuming a region of the state space produces informative data, and the system is sub-exponentially unstable, we establish non-asymptotic guarantees on the estimation error at times where the state trajectory evolves in this region. If the whole state space is informative, high probability guarantees on the error hold for all times. Examples are provided where our results are useful for analysis, but existing results are not. |
| title | Non-Asymptotic Bounds for Closed-Loop Identification of Unstable Nonlinear Stochastic Systems |
| topic | Systems and Control Machine Learning Optimization and Control |
| url | https://arxiv.org/abs/2412.04157 |