Kernel EDMD for data-driven nonlinear Koopman MPC with stability guarantees
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arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866912274100256768 |
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| author | Bold, Lea Schaller, Manuel Schimperna, Irene Worthmann, Karl |
| author_facet | Bold, Lea Schaller, Manuel Schimperna, Irene Worthmann, Karl |
| contents | Extended dynamic mode decomposition (EDMD) is a popular data-driven method to predict the action of the Koopman operator, i.e., the evolution of an observable function along the flow of a dynamical system. In this paper, we leverage a recently-introduced kernel EDMD method for control systems for data-driven model predictive control. Building upon pointwise error bounds proportional in the state, we rigorously show practical asymptotic stability of the origin w.r.t. the MPC closed loop without stabilizing terminal conditions. The key novelty is that we avoid restrictive invariance conditions. Last, we verify our findings by numerical simulations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_08709 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Kernel EDMD for data-driven nonlinear Koopman MPC with stability guarantees Bold, Lea Schaller, Manuel Schimperna, Irene Worthmann, Karl Optimization and Control Extended dynamic mode decomposition (EDMD) is a popular data-driven method to predict the action of the Koopman operator, i.e., the evolution of an observable function along the flow of a dynamical system. In this paper, we leverage a recently-introduced kernel EDMD method for control systems for data-driven model predictive control. Building upon pointwise error bounds proportional in the state, we rigorously show practical asymptotic stability of the origin w.r.t. the MPC closed loop without stabilizing terminal conditions. The key novelty is that we avoid restrictive invariance conditions. Last, we verify our findings by numerical simulations. |
| title | Kernel EDMD for data-driven nonlinear Koopman MPC with stability guarantees |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2501.08709 |