Kernel-based error bounds of bilinear Koopman surrogate models for nonlinear data-driven control
arXiv:2503.13407 · doi:10.1109/LCSYS.2025.3582630
Abstract
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.
Accepted for publication in IEEE Control Systems Letters (L-CSS)
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- An overview of Koopman-based control: From error bounds to closed-loop guarantees
- SafEDMD: A Koopman-based data-driven controller design framework for nonlinear dynamical systems
- Koopman-based control of nonlinear systems with closed-loop guarantees
- Koopman-based control using sum-of-squares optimization: Improved stability guarantees and data efficiency
- End-to-end guarantees for indirect data-driven control of bilinear systems with finite stochastic data