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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2403.10623 |
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| _version_ | 1866910368864927744 |
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| author | Lortie, Louis Dahdah, Steven Forbes, James Richard |
| author_facet | Lortie, Louis Dahdah, Steven Forbes, James Richard |
| contents | This paper presents a data-driven method to identify an asymptotically stable Koopman system from noisy data. In particular, the proposed approach combines approximations of the system's forward- and backward-in-time dynamics to reduce bias caused by noisy data while enforcing asymptotic stability. A Koopman model of an inherently asymptotically stable system can be unstable due to noisy data and a poor choice of lifting functions. To prevent identifying an unstable model, the proposed approach imposes an asymptotic stability constraint on the Koopman model. The proposed method is formulated as a semidefinite program and its performance is compared to state-of-the-art methods with a simulated Duffing oscillator dataset and experimental soft robot dataset. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_10623 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Forward-Backward Extended DMD with an Asymptotic Stability Constraint Lortie, Louis Dahdah, Steven Forbes, James Richard Systems and Control This paper presents a data-driven method to identify an asymptotically stable Koopman system from noisy data. In particular, the proposed approach combines approximations of the system's forward- and backward-in-time dynamics to reduce bias caused by noisy data while enforcing asymptotic stability. A Koopman model of an inherently asymptotically stable system can be unstable due to noisy data and a poor choice of lifting functions. To prevent identifying an unstable model, the proposed approach imposes an asymptotic stability constraint on the Koopman model. The proposed method is formulated as a semidefinite program and its performance is compared to state-of-the-art methods with a simulated Duffing oscillator dataset and experimental soft robot dataset. |
| title | Forward-Backward Extended DMD with an Asymptotic Stability Constraint |
| topic | Systems and Control |
| url | https://arxiv.org/abs/2403.10623 |