Kernel-Based Error Bounds of Bilinear Koopman Surrogate Models for Nonlinear Data-Driven Control

作者：Robin Strässer, Manuel Schaller, Julian Berberich, Karl Worthmann, Frank Allgöwer · 发表于：IEEE Control Systems Letters · 年份：2025 · DOI：10.1109/lcsys.2025.3582630 · 被引用次数：10 · 研究领域：Model Reduction and Neural Networks、Control Systems and Identification、Advanced Control Systems Optimization

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.