# Deep Learning of Koopman Representation for Control

arXiv: https://arxiv.org/abs/2010.07546 · HTML: https://mlsanity.com/paper/2010.07546/

## Key facts

- Cited by 26 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 15 Oct 2020.

## Built on by (most cited first, 26 of 26)

- [Koopman Neural Forecaster for Time Series with Temporal Distribution Shifts](https://mlsanity.com/paper/2210.03675/) (2022)
- [Deep Koopman Operator with Control for Nonlinear Systems](https://mlsanity.com/paper/2202.08004/) (2022)
- [Unsupervised Learning of Equivariant Structure from Sequences](https://mlsanity.com/paper/2210.05972/) (2022)
- [VCformer: Variable Correlation Transformer with Inherent Lagged Correlation for Multivariate Time Series Forecasting](https://mlsanity.com/paper/2405.11470/) (2024)
- [Efficient Dynamics Modeling in Interactive Environments with Koopman Theory](https://mlsanity.com/paper/2306.11941/) (2023)
- [Task-Oriented Koopman-Based Control with Contrastive Encoder](https://mlsanity.com/paper/2309.16077/) (2023)
- [ActionDiffusion: An Action-aware Diffusion Model for Procedure Planning in Instructional Videos](https://mlsanity.com/paper/2403.08591/) (2024)
- [RoboKoop: Efficient Control Conditioned Representations from Visual Input in Robotics using Koopman Operator](https://mlsanity.com/paper/2409.03107/) (2024)
- [Data-driven End-to-end Learning of Pole Placement Control for Nonlinear Dynamics via Koopman Invariant Subspaces](https://mlsanity.com/paper/2208.08883/) (2022)
- [Data-Driven Linear Koopman Embedding for Networked Systems: Model-Predictive Grid Control](https://mlsanity.com/paper/2206.01272/) (2022)
- [Physics-Informed Koopman Network](https://mlsanity.com/paper/2211.09419/) (2022)
- [CHyLL: Learning Continuous Neural Representations of Hybrid Systems](https://mlsanity.com/paper/2512.10117/) (2025)
- [Split Learning Meets Koopman Theory for Wireless Remote Monitoring and Prediction](https://mlsanity.com/paper/2104.08109/) (2021)
- [Learning Linear Embeddings for Non-Linear Network Dynamics with Koopman Message Passing](https://mlsanity.com/paper/2305.09060/) (2023)
- [Optimal Control of Nonlinear Systems with Unknown Dynamics](https://mlsanity.com/paper/2305.15188/) (2023)
- [Automated Global Analysis of Experimental Dynamics through Low-Dimensional Linear Embeddings](https://mlsanity.com/paper/2411.00989/) (2024)
- [KIPPO: Koopman-Inspired Proximal Policy Optimization](https://mlsanity.com/paper/2505.14566/) (2025)
- [MAKO: Meta-Adaptive Koopman Operators for Learning-based Model Predictive Control of Parametrically Uncertain Nonlinear Systems](https://mlsanity.com/paper/2510.09042/) (2025)
- [Supervised DKRC with Images for Offline System Identification](https://mlsanity.com/paper/2109.02241/) (2021)
- [Learned Lifted Linearization Applied to Unstable Dynamic Systems Enabled by Koopman Direct Encoding](https://mlsanity.com/paper/2210.13602/) (2022)
- [Analysis of Truncated Singular Value Decomposition for Koopman Operator-Based Lane Change Model](https://mlsanity.com/paper/2409.18586/) (2024)
- [Efficiently Scanning and Resampling Spatio-Temporal Tasks with Irregular Observations](https://mlsanity.com/paper/2410.08681/) (2024)
- [Deep Neural Koopman Operator-based Economic Model Predictive Control of Shipboard Carbon Capture System](https://mlsanity.com/paper/2504.06818/) (2025)
- [KoopCast: Trajectory Forecasting via Koopman Operators](https://mlsanity.com/paper/2509.15513/) (2025)
- [Deep Koopman Economic Model Predictive Control of a Pasteurisation Unit](https://mlsanity.com/paper/2511.04437/) (2025)
- [Efficient Reinforcement Learning using Linear Koopman Dynamics for Nonlinear Robotic Systems](https://mlsanity.com/paper/2604.19980/) (2026)

## Abstract (arXiv)

We develop a data-driven, model-free approach for the optimal control of the dynamical system. The proposed approach relies on the Deep Neural Network (DNN) based learning of Koopman operator for the purpose of control. In particular, DNN is employed for the data-driven identification of basis function used in the linear lifting of nonlinear control system dynamics. The controller synthesis is purely data-driven and does not rely on a priori domain knowledge. The OpenAI Gym environment, employed for Reinforcement Learning-based control design, is used for data generation and learning of Koopman operator in control setting. The method is applied to two classic dynamical systems on OpenAI Gym environment to demonstrate the capability.