mlsanityData to 7 Oct 2026

Linear quadratic control of nonlinear systems with Koopman operator learning and the Nystr"om method

arXiv 2403.02811 ↗First posted 5 Mar 2024math.OC cs.SY eess.SYcited by 2

Not on the map. Why?

Abstract (arXiv)

In this paper, we study how the Koopman operator framework can be combined with kernel methods to effectively control nonlinear dynamical systems. While kernel methods have typically large computational requirements, we show how random subspaces (Nystr"om approximation) can be used to achieve huge computational savings while preserving accuracy. Our main technical contribution is deriving theoretical guarantees on the effect of the Nystr"om approximation. More precisely, we study the linear quadratic regulator problem, showing that the approximated Riccati operator converges at the rate m-1/2, and the regulator objective, for the associated solution of the optimal control problem, converges at the rate m-1, where m is the random subspace size. Theoretical findings are complemented by numerical experiments corroborating our results.

Key facts. Cited by 2 papers in the map (data through 7 Oct 2026). Builds on 27 of its 57 references that are in the map. First posted on arXiv 5 Mar 2024.

Builds on

27 of 57 references.

References · 27

  1. 2016Kernel Mean Embedding of Distributions: A Review and Beyondcited by 360
  2. 2021Modern Koopman Theory for Dynamical Systemscited by 269
  3. 2018Global Convergence of Policy Gradient Methods for the Linear Quadratic Regulatorcited by 211
  4. 2018Learning Without Mixing: Towards A Sharp Analysis of Linear System Identificationcited by 158
  5. 2017On the Sample Complexity of the Linear Quadratic Regulatorcited by 151
  6. 2016Linear predictors for nonlinear dynamical systems: Koopman operator meets model predictive controlcited by 134
  7. 2015Less is More: Nystr"om Computational Regularizationcited by 89
  8. 2022Learning Dynamical Systems via Koopman Operator Regression in Reproducing Kernel Hilbert Spacescited by 66
  9. 2017Data-driven discovery of Koopman eigenfunctions for controlcited by 64
  10. 2016Generalizing Koopman Theory to allow for inputs and controlcited by 49
  11. 2017Eigendecompositions of Transfer Operators in Reproducing Kernel Hilbert Spacescited by 48
  12. 2021Koopman Operator Dynamical Models: Learning, Analysis and Controlcited by 42
15 more
  1. 2018Optimal construction of Koopman eigenfunctions for prediction and controlcited by 34
  2. 2017Koopman operator-based model reduction for switched-system control of PDEscited by 31
  3. 2019Active Learning of Dynamics for Data-Driven Control Using Koopman Operatorscited by 31
  4. 2020Kernel-based approximation of the Koopman generator and Schr"odinger operatorcited by 31
  5. 2021Finite-data error bounds for Koopman-based prediction and controlcited by 26
  6. 2022Deep Koopman Operator with Control for Nonlinear Systemscited by 25
  7. 2023Koopman Kernel Regressioncited by 22
  8. 2021Learning to Forecast Dynamical Systems from Streaming Datacited by 17
  9. 2023Estimating Koopman operators with sketching to provably learn large scale dynamical systemscited by 15
  10. 2017Model-Based Control Using Koopman Operatorscited by 14
  11. 2022Deep Koopman Learning of Nonlinear Time-Varying Systemscited by 10
  12. 2022Representer Theorem for Learning Koopman Operatorscited by 9
  13. 2023Sketch In, Sketch Out: Accelerating both Learning and Inference for Structured Prediction with Kernelscited by 5
  14. 2022Model Predictive Control for Dynamic Cloth Manipulation: Parameter Learning and Experimental Validationcited by 4
  15. 2021Controlled Gaussian Process Dynamical Models with Application to Robotic Cloth Manipulationcited by 1

Built on by

Cited by year

Citing papers per year: 2024: 2.

2 papers.

  1. 2024Nonparametric Control Koopman Operatorscited by 7
  2. 2024Data-Driven Stochastic Optimal Control in Reproducing Kernel Hilbert Spacescited by 2