A Koopman Operator Approach to Data-Driven Control of Semilinear Parabolic Systems
Fuente:
arXiv
Salvato in:
| Autori principali: | , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2025
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866909581746110464 |
|---|---|
| author | Deutscher, Joachim Enderes, Tarik |
| author_facet | Deutscher, Joachim Enderes, Tarik |
| contents | This paper is concerned with the data-driven stabilization of unknown boundary controlled semilinear parabolic systems. The nonlinear dynamics of the system are lifted using a finite number of eigenfunctionals of the Koopman operator related to the autonomous semilinear PDE. This results in a novel data-driven finite-dimensional model of the lifted dynamics, which is amenable to apply design procedures for finite-dimensional systems to stabilize the semilinear parabolic system. In order to facilitate this, a bilinearization of the lifted dynamics is considered and feedback linearization is applied for the data-driven stabilization of the semilinear parabolic PDE. This reveals a novel connection between the assignment of eigenfunctionals to the closed-loop Koopman operator and feedback linearization. By making use of a modal representation, exponential stability of the closed-loop system in the presence of errors resulting from the data-driven computation of eigenfunctionals and the bilinearization is verified. The data-driven controller directly follows from applying generalized eDMD to state data available for the semilinear parabolic PDE. An example of an unstable semilinear reaction-diffusion system with finite-time blow up demonstrates the novel data-driven stabilization approach. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_11959 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A Koopman Operator Approach to Data-Driven Control of Semilinear Parabolic Systems Deutscher, Joachim Enderes, Tarik Systems and Control This paper is concerned with the data-driven stabilization of unknown boundary controlled semilinear parabolic systems. The nonlinear dynamics of the system are lifted using a finite number of eigenfunctionals of the Koopman operator related to the autonomous semilinear PDE. This results in a novel data-driven finite-dimensional model of the lifted dynamics, which is amenable to apply design procedures for finite-dimensional systems to stabilize the semilinear parabolic system. In order to facilitate this, a bilinearization of the lifted dynamics is considered and feedback linearization is applied for the data-driven stabilization of the semilinear parabolic PDE. This reveals a novel connection between the assignment of eigenfunctionals to the closed-loop Koopman operator and feedback linearization. By making use of a modal representation, exponential stability of the closed-loop system in the presence of errors resulting from the data-driven computation of eigenfunctionals and the bilinearization is verified. The data-driven controller directly follows from applying generalized eDMD to state data available for the semilinear parabolic PDE. An example of an unstable semilinear reaction-diffusion system with finite-time blow up demonstrates the novel data-driven stabilization approach. |
| title | A Koopman Operator Approach to Data-Driven Control of Semilinear Parabolic Systems |
| topic | Systems and Control |
| url | https://arxiv.org/abs/2504.11959 |