# Learning to control switching nonlinear systems with Koopman operator regression

arXiv: https://arxiv.org/abs/2607.11344 · HTML: https://mlsanity.com/paper/2607.11344/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 27 of its 59 references that are in the map.
- First posted on arXiv 13 Jul 2026.

## Builds on (most cited first, 27 of 27)

- [Modern Koopman Theory for Dynamical Systems](https://mlsanity.com/paper/2102.12086/) (2021)
- [Linear predictors for nonlinear dynamical systems: Koopman operator meets model predictive control](https://mlsanity.com/paper/1611.03537/) (2016)
- [On Convergence of Extended Dynamic Mode Decomposition to the Koopman Operator](https://mlsanity.com/paper/1703.04680/) (2017)
- [Learning Dynamical Systems via Koopman Operator Regression in Reproducing Kernel Hilbert Spaces](https://mlsanity.com/paper/2205.14027/) (2022)
- [Statistical Learning Theory for Control: A Finite Sample Perspective](https://mlsanity.com/paper/2209.05423/) (2022)
- [Koopman Operator Dynamical Models: Learning, Analysis and Control](https://mlsanity.com/paper/2102.02522/) (2021)
- [Sharp Spectral Rates for Koopman Operator Learning](https://mlsanity.com/paper/2302.02004/) (2023)
- [Optimal construction of Koopman eigenfunctions for prediction and control](https://mlsanity.com/paper/1810.08733/) (2018)
- [Koopman operator-based model reduction for switched-system control of PDEs](https://mlsanity.com/paper/1710.06759/) (2017)
- [Kernel-based approximation of the Koopman generator and Schr"odinger operator](https://mlsanity.com/paper/2005.13231/) (2020)
- [Finite-data error bounds for Koopman-based prediction and control](https://mlsanity.com/paper/2108.07102/) (2021)
- [Koopman Kernel Regression](https://mlsanity.com/paper/2305.16215/) (2023)
- [Learning to Forecast Dynamical Systems from Streaming Data](https://mlsanity.com/paper/2109.09703/) (2021)
- [Optimal Rates for Vector-Valued Spectral Regularization Learning Algorithms](https://mlsanity.com/paper/2405.14778/) (2024)
- [Consistent Long-Term Forecasting of Ergodic Dynamical Systems](https://mlsanity.com/paper/2312.13426/) (2023)
- [An overview of Koopman-based control: From error bounds to closed-loop guarantees](https://mlsanity.com/paper/2509.02839/) (2025)
- [Representer Theorem for Learning Koopman Operators](https://mlsanity.com/paper/2208.01681/) (2022)
- [Data-driven MPC with stability guarantees using extended dynamic mode decomposition](https://mlsanity.com/paper/2308.00296/) (2023)
- [Nonparametric Control Koopman Operators](https://mlsanity.com/paper/2405.07312/) (2024)
- [Operator World Models for Reinforcement Learning](https://mlsanity.com/paper/2406.19861/) (2024)
- [Optimality Conditions for Model Predictive Control: Rethinking Predictive Model Design](https://mlsanity.com/paper/2412.18268/) (2024)
- [An overview of systems-theoretic guarantees in data-driven model predictive control](https://mlsanity.com/paper/2406.04130/) (2024)
- [On discount functions for economic model predictive control without terminal conditions](https://mlsanity.com/paper/2405.14361/) (2024)
- [Discounted MPC and infinite-horizon optimal control under plant-model mismatch: Stability and suboptimality](https://mlsanity.com/paper/2604.08521/) (2026)
- [Limitations of LTI Koopman Modeling for Nonlinear Control Systems](https://mlsanity.com/paper/2604.25290/) (2026)
- [Data-driven MPC with terminal conditions in the Koopman framework](https://mlsanity.com/paper/2408.12457/) (2024)
- [Koopman operator theory: fundamentals, control, and applications](https://mlsanity.com/paper/2607.01819/) (2026)

## Abstract (arXiv)

In this work, we consider the identification and control of nonlinear systems with finite action spaces. The unknown dynamics are estimated from finite samples with Koopman operator regression in a reproducing kernel Hilbert space, yielding a linear switching predictive model, the switches governed by the value of the control variable. In order to perform control in closed-loop, the learned dynamics are employed in an infinite-horizon optimal control problem with time-varying stage cost, which is solved by means of model predictive control. In a theoretical analysis, we derive learning rates for the Koopman dynamics approximation. We further quantify, under suitable assumptions, the sub-optimality of the model predictive control strategy, both in the case of exact Koopman dynamics, and in the case of learned ones. Numerical simulations on the Duffing oscillator complement our theoretical findings.