Finite Sample Identification of Partially Observed Bilinear Dynamical Systems
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866911224876236800 |
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| author | Sattar, Yahya Jedra, Yassir Fazel, Maryam Dean, Sarah |
| author_facet | Sattar, Yahya Jedra, Yassir Fazel, Maryam Dean, Sarah |
| contents | We consider the problem of learning a realization of a partially observed bilinear dynamical system (BLDS) from noisy input-output data. Given a single trajectory of input-output samples, we provide a finite time analysis for learning the system's Markov-like parameters, from which a balanced realization of the bilinear system can be obtained. Our bilinear system identification algorithm learns the system's Markov-like parameters by regressing the outputs to highly correlated, nonlinear, and heavy-tailed covariates. Moreover, the stability of BLDS depends on the sequence of inputs used to excite the system. These properties, unique to partially observed bilinear dynamical systems, pose significant challenges to the analysis of our algorithm for learning the unknown dynamics. We address these challenges and provide high probability error bounds on our identification algorithm under a uniform stability assumption. Our analysis provides insights into system theoretic quantities that affect learning accuracy and sample complexity. Lastly, we perform numerical experiments with synthetic data to reinforce these insights. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_07652 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Finite Sample Identification of Partially Observed Bilinear Dynamical Systems Sattar, Yahya Jedra, Yassir Fazel, Maryam Dean, Sarah Machine Learning Systems and Control Optimization and Control We consider the problem of learning a realization of a partially observed bilinear dynamical system (BLDS) from noisy input-output data. Given a single trajectory of input-output samples, we provide a finite time analysis for learning the system's Markov-like parameters, from which a balanced realization of the bilinear system can be obtained. Our bilinear system identification algorithm learns the system's Markov-like parameters by regressing the outputs to highly correlated, nonlinear, and heavy-tailed covariates. Moreover, the stability of BLDS depends on the sequence of inputs used to excite the system. These properties, unique to partially observed bilinear dynamical systems, pose significant challenges to the analysis of our algorithm for learning the unknown dynamics. We address these challenges and provide high probability error bounds on our identification algorithm under a uniform stability assumption. Our analysis provides insights into system theoretic quantities that affect learning accuracy and sample complexity. Lastly, we perform numerical experiments with synthetic data to reinforce these insights. |
| title | Finite Sample Identification of Partially Observed Bilinear Dynamical Systems |
| topic | Machine Learning Systems and Control Optimization and Control |
| url | https://arxiv.org/abs/2501.07652 |