Interpolation Conditions for Data Consistency and Prediction in Noisy Linear Systems
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866909901279723520 |
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| author | Vanelli, Martina Monshizadeh, Nima Hendrickx, Julien M. |
| author_facet | Vanelli, Martina Monshizadeh, Nima Hendrickx, Julien M. |
| contents | We develop an interpolation-based framework for noisy linear systems with unknown system matrix with bounded norm (implying bounded growth or non-increasing energy), and bounded process noise energy. The proposed approach characterizes all trajectories consistent with the measured data and these prior bounds in a purely data-driven manner. This characterization enables data-consistency verification, inference, and one-step ahead prediction, which can be leveraged for safety verification and cost minimization. Ultimately, this work represents a preliminary step toward exploiting interpolation conditions in data-driven control, offering a systematic way to characterize trajectories consistent with a dynamical system within a given class and enabling their use in control design. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_08484 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Interpolation Conditions for Data Consistency and Prediction in Noisy Linear Systems Vanelli, Martina Monshizadeh, Nima Hendrickx, Julien M. Systems and Control Machine Learning Optimization and Control We develop an interpolation-based framework for noisy linear systems with unknown system matrix with bounded norm (implying bounded growth or non-increasing energy), and bounded process noise energy. The proposed approach characterizes all trajectories consistent with the measured data and these prior bounds in a purely data-driven manner. This characterization enables data-consistency verification, inference, and one-step ahead prediction, which can be leveraged for safety verification and cost minimization. Ultimately, this work represents a preliminary step toward exploiting interpolation conditions in data-driven control, offering a systematic way to characterize trajectories consistent with a dynamical system within a given class and enabling their use in control design. |
| title | Interpolation Conditions for Data Consistency and Prediction in Noisy Linear Systems |
| topic | Systems and Control Machine Learning Optimization and Control |
| url | https://arxiv.org/abs/2504.08484 |