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Learning to control switching nonlinear systems with Koopman operator regression

arXiv 2607.11344 ↗First posted 13 Jul 2026math.OC cs.SY eess.SYcited by 0

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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.

Key facts. No citing papers in the map yet (data through 7 Oct 2026). Builds on 27 of its 59 references that are in the map. First posted on arXiv 13 Jul 2026.

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References · 27

  1. 2021Modern Koopman Theory for Dynamical Systemscited by 269
  2. 2016Linear predictors for nonlinear dynamical systems: Koopman operator meets model predictive controlcited by 134
  3. 2017On Convergence of Extended Dynamic Mode Decomposition to the Koopman Operatorcited by 70
  4. 2022Learning Dynamical Systems via Koopman Operator Regression in Reproducing Kernel Hilbert Spacescited by 66
  5. 2022Statistical Learning Theory for Control: A Finite Sample Perspectivecited by 52
  6. 2021Koopman Operator Dynamical Models: Learning, Analysis and Controlcited by 42
  7. 2023Sharp Spectral Rates for Koopman Operator Learningcited by 35
  8. 2018Optimal construction of Koopman eigenfunctions for prediction and controlcited by 34
  9. 2017Koopman operator-based model reduction for switched-system control of PDEscited by 31
  10. 2020Kernel-based approximation of the Koopman generator and Schr"odinger operatorcited by 31
  11. 2021Finite-data error bounds for Koopman-based prediction and controlcited by 26
  12. 2023Koopman Kernel Regressioncited by 22
15 more
  1. 2021Learning to Forecast Dynamical Systems from Streaming Datacited by 17
  2. 2024Optimal Rates for Vector-Valued Spectral Regularization Learning Algorithmscited by 12
  3. 2023Consistent Long-Term Forecasting of Ergodic Dynamical Systemscited by 10
  4. 2022Representer Theorem for Learning Koopman Operatorscited by 9
  5. 2025An overview of Koopman-based control: From error bounds to closed-loop guaranteescited by 9
  6. 2023Data-driven MPC with stability guarantees using extended dynamic mode decompositioncited by 7
  7. 2024Nonparametric Control Koopman Operatorscited by 7
  8. 2024Operator World Models for Reinforcement Learningcited by 7
  9. 2024Optimality Conditions for Model Predictive Control: Rethinking Predictive Model Designcited by 4
  10. 2024An overview of systems-theoretic guarantees in data-driven model predictive controlcited by 3
  11. 2024On discount functions for economic model predictive control without terminal conditionscited by 2
  12. 2026Discounted MPC and infinite-horizon optimal control under plant-model mismatch: Stability and suboptimalitycited by 2
  13. 2026Limitations of LTI Koopman Modeling for Nonlinear Control Systemscited by 2
  14. 2024Data-driven MPC with terminal conditions in the Koopman frameworkcited by 1
  15. 2026Koopman operator theory: fundamentals, control, and applicationscited by 1

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