Kernel-based error bounds of bilinear Koopman surrogate models for nonlinear data-driven control
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arXiv
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| Main Authors: | , , , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866915405347422208 |
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| author | Strässer, Robin Schaller, Manuel Berberich, Julian Worthmann, Karl Allgöwer, Frank |
| author_facet | Strässer, Robin Schaller, Manuel Berberich, Julian Worthmann, Karl Allgöwer, Frank |
| contents | We derive novel deterministic bounds on the approximation error of data-based bilinear surrogate models for unknown nonlinear systems. The surrogate models are constructed using kernel-based extended dynamic mode decomposition to approximate the Koopman operator in a reproducing kernel Hilbert space. Unlike previous methods that require restrictive assumptions on the invariance of the dictionary, our approach leverages kernel-based dictionaries that allow us to control the projection error via pointwise error bounds, overcoming a significant limitation of existing theoretical guarantees. The derived state- and input-dependent error bounds allow for direct integration into Koopman-based robust controller designs with closed-loop guarantees for the unknown nonlinear system. Numerical examples illustrate the effectiveness of the proposed framework. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_13407 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Kernel-based error bounds of bilinear Koopman surrogate models for nonlinear data-driven control Strässer, Robin Schaller, Manuel Berberich, Julian Worthmann, Karl Allgöwer, Frank Systems and Control Optimization and Control We derive novel deterministic bounds on the approximation error of data-based bilinear surrogate models for unknown nonlinear systems. The surrogate models are constructed using kernel-based extended dynamic mode decomposition to approximate the Koopman operator in a reproducing kernel Hilbert space. Unlike previous methods that require restrictive assumptions on the invariance of the dictionary, our approach leverages kernel-based dictionaries that allow us to control the projection error via pointwise error bounds, overcoming a significant limitation of existing theoretical guarantees. The derived state- and input-dependent error bounds allow for direct integration into Koopman-based robust controller designs with closed-loop guarantees for the unknown nonlinear system. Numerical examples illustrate the effectiveness of the proposed framework. |
| title | Kernel-based error bounds of bilinear Koopman surrogate models for nonlinear data-driven control |
| topic | Systems and Control Optimization and Control |
| url | https://arxiv.org/abs/2503.13407 |