# Kernel-based error bounds of bilinear Koopman surrogate models for nonlinear data-driven control

arXiv: https://arxiv.org/abs/2503.13407 · HTML: https://mlsanity.com/paper/2503.13407/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 17 Mar 2025.

## Built on by (most cited first, 2 of 2)

- [Koopman operator theory: fundamentals, control, and applications](https://mlsanity.com/paper/2607.01819/) (2026)
- [On Data-Driven Koopman Representations of Nonlinear Delay Differential Equations](https://mlsanity.com/paper/2604.03086/) (2026)

## Abstract (arXiv)

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.