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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| Online Access: | https://arxiv.org/abs/2408.06607 |
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| _version_ | 1866912547626549248 |
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| author | Sakib, Shahriar Akbar Pan, Shaowu |
| author_facet | Sakib, Shahriar Akbar Pan, Shaowu |
| contents | We propose a noise-robust learning framework for the Koopman operator of nonlinear dynamical systems, with guaranteed long-term stability and improved model performance for better model-based predictive control tasks. Unlike some existing approaches that rely on ad hoc observables or black-box neural networks in extended dynamic mode decomposition (EDMD), our framework leverages observables generated by the system dynamics, when the system dynamics is known, through a Hankel matrix, which shares similarities with discrete Polyflow. When system dynamics is unknown, we approximate them with a neural network while maintaining structural similarities to discrete Polyflow. To enhance noise robustness and ensure long-term stability, we developed a stable parameterization of the Koopman operator, along with a progressive learning strategy for rollout loss. To further improve the performance of the model in the phase space, a simple iterative data augmentation strategy was developed. Numerical experiments of prediction and control of classic nonlinear systems with ablation study showed the effectiveness of the proposed techniques over several state-of-the-art practices. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_06607 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Learning Noise-Robust Stable Koopman Operator for Control with Hankel DMD Sakib, Shahriar Akbar Pan, Shaowu Dynamical Systems Machine Learning 37N35, 93B45 J.2 We propose a noise-robust learning framework for the Koopman operator of nonlinear dynamical systems, with guaranteed long-term stability and improved model performance for better model-based predictive control tasks. Unlike some existing approaches that rely on ad hoc observables or black-box neural networks in extended dynamic mode decomposition (EDMD), our framework leverages observables generated by the system dynamics, when the system dynamics is known, through a Hankel matrix, which shares similarities with discrete Polyflow. When system dynamics is unknown, we approximate them with a neural network while maintaining structural similarities to discrete Polyflow. To enhance noise robustness and ensure long-term stability, we developed a stable parameterization of the Koopman operator, along with a progressive learning strategy for rollout loss. To further improve the performance of the model in the phase space, a simple iterative data augmentation strategy was developed. Numerical experiments of prediction and control of classic nonlinear systems with ablation study showed the effectiveness of the proposed techniques over several state-of-the-art practices. |
| title | Learning Noise-Robust Stable Koopman Operator for Control with Hankel DMD |
| topic | Dynamical Systems Machine Learning 37N35, 93B45 J.2 |
| url | https://arxiv.org/abs/2408.06607 |