Robust Nonlinear System Identification in Reproducing Kernel Hilbert Spaces via Scenario Optimization
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866917388296912896 |
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| author | Lübsen, Jannis Eichler, Annika |
| author_facet | Lübsen, Jannis Eichler, Annika |
| contents | This paper proposes a method for constructing one-step prediction tubes for nonlinear systems using reproducing kernel Hilbert spaces. We approximate a bounded reproducing kernel Hilbert space (RKHS) hypothesis set by a finite-dimensional subspace using bounds based on n-widths and a greedy algorithm for basis reduction. For kernels whose native spaces are norm-equivalent to Sobolev spaces, we derive how the required basis size scales with kernel smoothness and input dimension. This finite-dimensional representation enables the use of convex scenario optimization to obtain violation guarantees for the learned predictor without requiring an a priori bound on the true system's RKHS norm or Lipschitz constant. The method is demonstrated on an obstacle-avoidance task. We also discuss the main limitations of the current analysis, including dimensional scaling and dependence on i.i.d. data. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2604_05798 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Robust Nonlinear System Identification in Reproducing Kernel Hilbert Spaces via Scenario Optimization Lübsen, Jannis Eichler, Annika Systems and Control This paper proposes a method for constructing one-step prediction tubes for nonlinear systems using reproducing kernel Hilbert spaces. We approximate a bounded reproducing kernel Hilbert space (RKHS) hypothesis set by a finite-dimensional subspace using bounds based on n-widths and a greedy algorithm for basis reduction. For kernels whose native spaces are norm-equivalent to Sobolev spaces, we derive how the required basis size scales with kernel smoothness and input dimension. This finite-dimensional representation enables the use of convex scenario optimization to obtain violation guarantees for the learned predictor without requiring an a priori bound on the true system's RKHS norm or Lipschitz constant. The method is demonstrated on an obstacle-avoidance task. We also discuss the main limitations of the current analysis, including dimensional scaling and dependence on i.i.d. data. |
| title | Robust Nonlinear System Identification in Reproducing Kernel Hilbert Spaces via Scenario Optimization |
| topic | Systems and Control |
| url | https://arxiv.org/abs/2604.05798 |