A Koopman-backstepping approach to data-driven robust output regulation for linear parabolic systems
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arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866908397563019264 |
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| author | Deutscher, Joachim Zimmer, Julian |
| author_facet | Deutscher, Joachim Zimmer, Julian |
| contents | In this paper a solution of the data-driven robust output regulation problem for linear parabolic systems is presented. Both the system as well as the ODE, i.e., the disturbance model, describing the disturbances are unknown, but finite-time sequential data obtained from measurements of the output to be controlled and additional boundary outputs are available. The data-driven controller is designed in the Koopman operator framework for PDEs, where the Koopman modes and eigenvalues are obtained from data using Hankel-DMD. It is shown that all system parameters and the eigenvalues of the disturbance model can be recovered from the available measurements by solving an inverse Sturm-Liouville problem. This allows to directly apply backstepping methods for the robust regulator design. For this, closed-loop stability in the presence of small errors in the Hankel-DMD is verified in the nominal case. Robust output regulation is shown for non-destabilizing model uncertainties. A numerical example demonstrates the results of the paper. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_06451 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A Koopman-backstepping approach to data-driven robust output regulation for linear parabolic systems Deutscher, Joachim Zimmer, Julian Systems and Control In this paper a solution of the data-driven robust output regulation problem for linear parabolic systems is presented. Both the system as well as the ODE, i.e., the disturbance model, describing the disturbances are unknown, but finite-time sequential data obtained from measurements of the output to be controlled and additional boundary outputs are available. The data-driven controller is designed in the Koopman operator framework for PDEs, where the Koopman modes and eigenvalues are obtained from data using Hankel-DMD. It is shown that all system parameters and the eigenvalues of the disturbance model can be recovered from the available measurements by solving an inverse Sturm-Liouville problem. This allows to directly apply backstepping methods for the robust regulator design. For this, closed-loop stability in the presence of small errors in the Hankel-DMD is verified in the nominal case. Robust output regulation is shown for non-destabilizing model uncertainties. A numerical example demonstrates the results of the paper. |
| title | A Koopman-backstepping approach to data-driven robust output regulation for linear parabolic systems |
| topic | Systems and Control |
| url | https://arxiv.org/abs/2506.06451 |