# Learning Noise-Robust Stable Koopman Operator for Control with Hankel DMD

arXiv: https://arxiv.org/abs/2408.06607 · HTML: https://mlsanity.com/paper/2408.06607/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 29 of its 70 references that are in the map.
- First posted on arXiv 13 Aug 2024.

## Builds on (most cited first, 29 of 29)

- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Cyclical Learning Rates for Training Neural Networks](https://mlsanity.com/paper/1506.01186/) (2015)
- [Deep learning for universal linear embeddings of nonlinear dynamics](https://mlsanity.com/paper/1712.09707/) (2017)
- [Modern Koopman Theory for Dynamical Systems](https://mlsanity.com/paper/2102.12086/) (2021)
- [Linearly-Recurrent Autoencoder Networks for Learning Dynamics](https://mlsanity.com/paper/1712.01378/) (2017)
- [Linear predictors for nonlinear dynamical systems: Koopman operator meets model predictive control](https://mlsanity.com/paper/1611.03537/) (2016)
- [Data-driven discovery of Koopman eigenfunctions for control](https://mlsanity.com/paper/1707.01146/) (2017)
- [panda-gym: Open-source goal-conditioned environments for robotic learning](https://mlsanity.com/paper/2106.13687/) (2021)
- [Physics-Informed Probabilistic Learning of Linear Embeddings of Non-linear Dynamics With Guaranteed Stability](https://mlsanity.com/paper/1906.03663/) (2019)
- [Koopman Operator Dynamical Models: Learning, Analysis and Control](https://mlsanity.com/paper/2102.02522/) (2021)
- [Koopman Kernel Regression](https://mlsanity.com/paper/2305.16215/) (2023)
- [Data informativity: a new perspective on data-driven analysis and control](https://mlsanity.com/paper/1908.00468/) (2019)
- [Advantages of Bilinear Koopman Realizations for the Modeling and Control of Systems with Unknown Dynamics](https://mlsanity.com/paper/2010.09961/) (2020)
- [Data-Driven Model Predictive Control using Interpolated Koopman Generators](https://mlsanity.com/paper/2003.07094/) (2020)
- [Derivative-Based Koopman Operators for Real-Time Control of Robotic Systems](https://mlsanity.com/paper/2010.05778/) (2020)
- [Diffeomorphically Learning Stable Koopman Operators](https://mlsanity.com/paper/2112.04085/) (2021)
- [Deep Koopman Learning of Nonlinear Time-Varying Systems](https://mlsanity.com/paper/2210.06272/) (2022)
- [Operator inference with roll outs for learning reduced models from scarce and low-quality data](https://mlsanity.com/paper/2212.01418/) (2022)
- [Koopman-Assisted Reinforcement Learning](https://mlsanity.com/paper/2403.02290/) (2024)
- [Adversarial dynamical systems characterize when data-driven learning succeeds or fails](https://mlsanity.com/paper/2407.06312/) (2024)
- [Learning the Koopman Eigendecomposition: A Diffeomorphic Approach](https://mlsanity.com/paper/2110.07786/) (2021)
- [Learning Bilinear Models of Actuated Koopman Generators from Partially-Observed Trajectories](https://mlsanity.com/paper/2209.09977/) (2022)
- [Koopman-based Control of a Soft Continuum Manipulator Under Variable Loading Conditions](https://mlsanity.com/paper/2002.01407/) (2020)
- [Stable Dynamic Mode Decomposition Algorithm for Noisy Pressure-Sensitive Paint Measurement Data](https://mlsanity.com/paper/2107.11999/) (2021)
- [Online Real-time Learning of Dynamical Systems from Noisy Streaming Data: A Koopman Operator Approach](https://mlsanity.com/paper/2212.05259/) (2022)
- [Non-local Linearization of Nonlinear Differential Equations via Polyflows](https://mlsanity.com/paper/1902.04507/) (2019)
- [Immersion-based model predictive control of constrained nonlinear systems: Polyflow approximation](https://mlsanity.com/paper/2011.13255/) (2020)
- [Control-aware Learning of Koopman Embedding Models](https://mlsanity.com/paper/2209.08637/) (2022)
- [Practical Guidelines for Data-driven Identification of Lifted Linear Predictors for Control](https://mlsanity.com/paper/2408.01116/) (2024)

## Built on by (most cited first, 1 of 1)

- [A Dynamic Recurrent Adjacency Memory Network for Mixed-Generation Power System Stability Forecasting](https://mlsanity.com/paper/2511.03746/) (2025)

## Abstract (arXiv)

We propose a noise-robust learning framework for the Koopman operator of nonlinear dynamical systems, with guaranteed long-term stability and improved model performance for better model-based predictive control tasks. Unlike some existing approaches that rely on ad hoc observables or black-box neural networks in extended dynamic mode decomposition (EDMD), our framework leverages observables generated by the system dynamics, when the system dynamics is known, through a Hankel matrix, which shares similarities with discrete Polyflow. When system dynamics is unknown, we approximate them with a neural network while maintaining structural similarities to discrete Polyflow. To enhance noise robustness and ensure long-term stability, we developed a stable parameterization of the Koopman operator, along with a progressive learning strategy for rollout loss. To further improve the performance of the model in the phase space, a simple iterative data augmentation strategy was developed. Numerical experiments of prediction and control of classic nonlinear systems with ablation study showed the effectiveness of the proposed techniques over several state-of-the-art practices.