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

arXiv: https://arxiv.org/abs/2402.03145 · HTML: https://mlsanity.com/paper/2402.03145/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 38 of its 77 references that are in the map.
- First posted on arXiv 5 Feb 2024.

## Builds on (most cited first, 30 of 38)

- [Convex optimization](https://mlsanity.com/paper/2106.01946/) (2021)
- [Learning Koopman Invariant Subspaces for Dynamic Mode Decomposition](https://mlsanity.com/paper/1710.04340/) (2017)
- [Neural Lyapunov Control](https://mlsanity.com/paper/2005.00611/) (2020)
- [Linear predictors for nonlinear dynamical systems: Koopman operator meets model predictive control](https://mlsanity.com/paper/1611.03537/) (2016)
- [Learning Deep Neural Network Representations for Koopman Operators of Nonlinear Dynamical Systems](https://mlsanity.com/paper/1708.06850/) (2017)
- [Forecasting Sequential Data using Consistent Koopman Autoencoders](https://mlsanity.com/paper/2003.02236/) (2020)
- [Training robust neural networks using Lipschitz bounds](https://mlsanity.com/paper/2005.02929/) (2020)
- [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)
- [Generalizing Koopman Theory to allow for inputs and control](https://mlsanity.com/paper/1602.07647/) (2016)
- [Rigorous data-driven computation of spectral properties of Koopman operators for dynamical systems](https://mlsanity.com/paper/2111.14889/) (2021)
- [Koopman Operator Dynamical Models: Learning, Analysis and Control](https://mlsanity.com/paper/2102.02522/) (2021)
- [Optimal construction of Koopman eigenfunctions for prediction and control](https://mlsanity.com/paper/1810.08733/) (2018)
- [Finite-data error bounds for Koopman-based prediction and control](https://mlsanity.com/paper/2108.07102/) (2021)
- [The Multiverse of Dynamic Mode Decomposition Algorithms](https://mlsanity.com/paper/2312.00137/) (2023)
- [Deep Koopman Operator with Control for Nonlinear Systems](https://mlsanity.com/paper/2202.08004/) (2022)
- [Data-Driven Model Predictive Control using Interpolated Koopman Generators](https://mlsanity.com/paper/2003.07094/) (2020)
- [Koopman Form of Nonlinear Systems with Inputs](https://mlsanity.com/paper/2207.12132/) (2022)
- [A kernel-based approach to molecular conformation analysis](https://mlsanity.com/paper/1809.11092/) (2018)
- [Neural Stochastic Control](https://mlsanity.com/paper/2209.07240/) (2022)
- [Data-driven MPC with stability guarantees using extended dynamic mode decomposition](https://mlsanity.com/paper/2308.00296/) (2023)
- [Identification of MIMO Wiener-type Koopman Models for Data-Driven Model Reduction using Deep Learning](https://mlsanity.com/paper/2201.12669/) (2022)
- [Learning Bilinear Models of Actuated Koopman Generators from Partially-Observed Trajectories](https://mlsanity.com/paper/2209.09977/) (2022)
- [Robust data-driven control for nonlinear systems using the Koopman operator](https://mlsanity.com/paper/2304.03519/) (2023)
- [Generalizing Dynamic Mode Decomposition: Balancing Accuracy and Expressiveness in Koopman Approximations](https://mlsanity.com/paper/2108.03712/) (2021)
- [Reprojection methods for Koopman-based modelling and prediction](https://mlsanity.com/paper/2307.16188/) (2023)
- [Koopman-based feedback design with stability guarantees](https://mlsanity.com/paper/2312.01441/) (2023)
- [Feedback Stabilization Using Koopman Operator](https://mlsanity.com/paper/1810.00089/) (2018)
- [Towards reliable data-based optimal and predictive control using extended DMD](https://mlsanity.com/paper/2202.09084/) (2022)
- [Guarantees for data-driven control of nonlinear systems using semidefinite programming: A survey](https://mlsanity.com/paper/2306.16042/) (2023)

## Built on by (most cited first, 5 of 5)

- [From Product Hilbert Spaces to the Generalized Koopman Operator and the Nonlinear Fundamental Lemma](https://mlsanity.com/paper/2508.07494/) (2025)
- [End-to-end guarantees for indirect data-driven control of bilinear systems with finite stochastic data](https://mlsanity.com/paper/2409.18010/) (2024)
- [Koopman operator theory: fundamentals, control, and applications](https://mlsanity.com/paper/2607.01819/) (2026)
- [Beyond Linear Dynamics: Neural Bilinear Dynamical Models for Time Series Forecasting](https://mlsanity.com/paper/2608.04471/) (2026)
- [Predefined-Time Resilient Integral Reinforcement Learning for Input-Constrained Unknown Nonlinear Systems Under FDI Attacks and Disturbances: A Fully Data-Driven Approach](https://mlsanity.com/paper/2609.11815/) (2026)

## 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.