mlsanityData to 7 Oct 2026

SafEDMD: A Koopman-based data-driven controller design framework for nonlinear dynamical systems

arXiv 2402.03145 ↗First posted 5 Feb 2024eess.SY cs.LG cs.SYcited by 4

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Abstract (arXiv)

The Koopman operator serves as the theoretical backbone for machine learning of dynamical control systems, where the operator is heuristically approximated by extended dynamic mode decomposition (EDMD). In this paper, we propose SafEDMD, a novel stability- and feedback-oriented EDMD-based controller design framework. Our approach leverages a reliable surrogate model generated in a data-driven fashion in order to provide closed-loop guarantees. In particular, we establish a controller design based on semi-definite programming with guaranteed stabilization of the underlying nonlinear system. As central ingredient, we derive proportional error bounds that vanish at the origin and are tailored to control tasks. We illustrate the developed method by means of several benchmark examples and highlight the advantages over state-of-the-art methods.

Key facts. Cited by 4 papers in the map (data through 7 Oct 2026). Builds on 38 of its 77 references that are in the map. First posted on arXiv 5 Feb 2024.

Builds on

38 of 77 references.

References · 38

  1. 2021Convex optimizationcited by 2,479
  2. 2017Learning Koopman Invariant Subspaces for Dynamic Mode Decompositioncited by 156
  3. 2020Neural Lyapunov Controlcited by 142
  4. 2016Linear predictors for nonlinear dynamical systems: Koopman operator meets model predictive controlcited by 134
  5. 2017Learning Deep Neural Network Representations for Koopman Operators of Nonlinear Dynamical Systemscited by 125
  6. 2020Forecasting Sequential Data using Consistent Koopman Autoencoderscited by 114
  7. 2020Training robust neural networks using Lipschitz boundscited by 98
  8. 2017On Convergence of Extended Dynamic Mode Decomposition to the Koopman Operatorcited by 70
  9. 2022Learning Dynamical Systems via Koopman Operator Regression in Reproducing Kernel Hilbert Spacescited by 66
  10. 2016Generalizing Koopman Theory to allow for inputs and controlcited by 49
  11. 2021Rigorous data-driven computation of spectral properties of Koopman operators for dynamical systemscited by 44
  12. 2021Koopman Operator Dynamical Models: Learning, Analysis and Controlcited by 42
26 more
  1. 2018Optimal construction of Koopman eigenfunctions for prediction and controlcited by 34
  2. 2021Finite-data error bounds for Koopman-based prediction and controlcited by 26
  3. 2022Deep Koopman Operator with Control for Nonlinear Systemscited by 25
  4. 2023The Multiverse of Dynamic Mode Decomposition Algorithmscited by 24
  5. 2020Data-Driven Model Predictive Control using Interpolated Koopman Generatorscited by 17
  6. 2022Koopman Form of Nonlinear Systems with Inputscited by 10
  7. 2018A kernel-based approach to molecular conformation analysiscited by 8
  8. 2022Neural Stochastic Controlcited by 8
  9. 2023Data-driven MPC with stability guarantees using extended dynamic mode decompositioncited by 7
  10. 2022Identification of MIMO Wiener-type Koopman Models for Data-Driven Model Reduction using Deep Learningcited by 6
  11. 2022Learning Bilinear Models of Actuated Koopman Generators from Partially-Observed Trajectoriescited by 6
  12. 2021Generalizing Dynamic Mode Decomposition: Balancing Accuracy and Expressiveness in Koopman Approximationscited by 5
  13. 2023Robust data-driven control for nonlinear systems using the Koopman operatorcited by 5
  14. 2023Reprojection methods for Koopman-based modelling and predictioncited by 5
  15. 2023Koopman-based feedback design with stability guaranteescited by 5
  16. 2018Feedback Stabilization Using Koopman Operatorcited by 4
  17. 2022Towards reliable data-based optimal and predictive control using extended DMDcited by 4
  18. 2023Guarantees for data-driven control of nonlinear systems using semidefinite programming: A surveycited by 4
  19. 2023Computationally Efficient Data-Driven Discovery and Linear Representation of Nonlinear Systems For Controlcited by 4
  20. 2021Dynamic Mode Decomposition with Control Liouville Operatorscited by 3
  21. 2021ACD-EDMD: Analytical Construction for Dictionaries of Lifting Functions in Koopman Operator-based Nonlinear Robotic Systemscited by 3
  22. 2023A structure exploiting SDP solver for robust controller synthesiscited by 3
  23. 2020Data-Driven Control of Nonlinear Systems: Beyond Polynomial Dynamicscited by 2
  24. 2022Direct data-driven LPV control of nonlinear systems: An experimental resultcited by 2
  25. 2023Control of bilinear systems using gain-scheduling: Stability and performance guaranteescited by 2
  26. 2023Decrypting Nonlinearity: Koopman Interpretation and Analysis of Cryptosystemscited by 1

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2024: 1; 2025: 1; 2026: 2.

4 papers.

  1. 2025From Product Hilbert Spaces to the Generalized Koopman Operator and the Nonlinear Fundamental Lemmacited by 2
  2. 2024End-to-end guarantees for indirect data-driven control of bilinear systems with finite stochastic datacited by 1
  3. 2026Koopman operator theory: fundamentals, control, and applicationscited by 1
  4. 2026Beyond Linear Dynamics: Neural Bilinear Dynamical Models for Time Series Forecastingcited by 0