# Kernel-based Koopman approximants for control: Flexible sampling, error analysis, and stability

arXiv: https://arxiv.org/abs/2412.02811 · HTML: https://mlsanity.com/paper/2412.02811/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 3 Dec 2024.

## Built on by (most cited first, 4 of 4)

- [Koopman operator theory: fundamentals, control, and applications](https://mlsanity.com/paper/2607.01819/) (2026)
- [Verifiable Regularity Criterion for Conditional Expectation Operators and Conditional Mean Embeddings with Applications to Nonparametric Regression, Bayesian Inverse Problems, and Koopman Operators](https://mlsanity.com/paper/2608.06155/) (2026)
- [Nonparametric Sparse Online Learning of the Koopman Operator](https://mlsanity.com/paper/2501.16489/) (2025)
- [On Data-Driven Koopman Representations of Nonlinear Delay Differential Equations](https://mlsanity.com/paper/2604.03086/) (2026)

## Abstract (arXiv)

Data-driven techniques for analysis, modeling, and control of complex dynamical systems are on the uptake. Koopman theory provides the theoretical foundation for the popular kernel extended dynamic mode decomposition (kEDMD). In this work, we propose a novel kEDMD scheme to approximate nonlinear control systems accompanied by an in-depth error analysis. Key features are regularization-based robustness and an adroit decomposition into micro and macro grids enabling flexible sampling. But foremost, we prove proportionality, i.e., explicit dependence on the distance to the (controlled) equilibrium, of the derived bound on the full approximation error. Leveraging this key property, we rigorously show that asymptotic stability of the data-driven surrogate (control) system implies asymptotic stability of the original (control) system and vice versa.