# Active Learning of Dynamics for Data-Driven Control Using Koopman Operators

arXiv: https://arxiv.org/abs/1906.05194 · HTML: https://mlsanity.com/paper/1906.05194/

## Key facts

- Cited by 32 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 12 Jun 2019.

## Built on by (most cited first, 30 of 32)

- [Koopman neural operator as a mesh-free solver of non-linear partial differential equations](https://mlsanity.com/paper/2301.10022/) (2023)
- [Active Learning of Discrete-Time Dynamics for Uncertainty-Aware Model Predictive Control](https://mlsanity.com/paper/2210.12583/) (2022)
- [Neural Koopman Lyapunov Control](https://mlsanity.com/paper/2201.05098/) (2022)
- [PyKoopman: A Python Package for Data-Driven Approximation of the Koopman Operator](https://mlsanity.com/paper/2306.12962/) (2023)
- [KoopmanLab: machine learning for solving complex physics equations](https://mlsanity.com/paper/2301.01104/) (2023)
- [Koopman operators with intrinsic observables in rigged reproducing kernel Hilbert spaces](https://mlsanity.com/paper/2403.02524/) (2024)
- [Koopman Spectrum Nonlinear Regulators and Efficient Online Learning](https://mlsanity.com/paper/2106.15775/) (2021)
- [Fast Ergodic Search with Kernel Functions](https://mlsanity.com/paper/2403.01536/) (2024)
- [Online Estimation of the Koopman Operator Using Fourier Features](https://mlsanity.com/paper/2212.01503/) (2022)
- [Online Control-Informed Learning](https://mlsanity.com/paper/2410.03924/) (2024)
- [Online Real-time Learning of Dynamical Systems from Noisy Streaming Data: A Koopman Operator Approach](https://mlsanity.com/paper/2212.05259/) (2022)
- [Active Visual Localization for Multi-Agent Collaboration: A Data-Driven Approach](https://mlsanity.com/paper/2310.02650/) (2023)
- [Dynamics Harmonic Analysis of Robotic Systems: Application in Data-Driven Koopman Modelling](https://mlsanity.com/paper/2312.07457/) (2023)
- [Linear Matrix Inequality Approaches to Koopman Operator Approximation](https://mlsanity.com/paper/2102.03613/) (2021)
- [System Norm Regularization Methods for Koopman Operator Approximation](https://mlsanity.com/paper/2110.09658/) (2021)
- [Auxiliary Functions as Koopman Observables: Data-Driven Analysis of Dynamical Systems via Polynomial Optimization](https://mlsanity.com/paper/2303.01483/) (2023)
- [Linear quadratic control of nonlinear systems with Koopman operator learning and the Nystr"om method](https://mlsanity.com/paper/2403.02811/) (2024)
- [A purely data-driven framework for prediction, optimization, and control of networked processes: application to networked SIS epidemic model](https://mlsanity.com/paper/2108.02005/) (2021)
- [Closed-Loop Koopman Operator Approximation](https://mlsanity.com/paper/2303.15318/) (2023)
- [Inferring Inference](https://mlsanity.com/paper/2310.03186/) (2023)
- [Uncertainty Modelling and Robust Observer Synthesis using the Koopman Operator](https://mlsanity.com/paper/2410.01057/) (2024)
- [Shared Control with Black Box Agents using Oracle Queries](https://mlsanity.com/paper/2410.19612/) (2024)
- [Kalman Filter Aided Federated Koopman Learning](https://mlsanity.com/paper/2507.04808/) (2025)
- [KoopMotion: Learning Almost Divergence Free Koopman Flow Fields for Motion Planning](https://mlsanity.com/paper/2509.09074/) (2025)
- [Adaptive Digital Twin of Sheet Metal Forming via Proper Orthogonal Decomposition-Based Koopman Operator with Model Predictive Control](https://mlsanity.com/paper/2511.10852/) (2025)
- [Thompson Sampling-Based Learning and Control for Unknown Dynamic Systems](https://mlsanity.com/paper/2506.22186/) (2025)
- [Sparse-mode Dynamic Mode Decomposition for Disambiguating Local and Global Structures](https://mlsanity.com/paper/2507.19787/) (2025)
- [Comprehensive Robust Dynamic Mode Decomposition from Mode Extraction to Dimensional Reduction](https://mlsanity.com/paper/2601.11116/) (2026)
- [Generalized Information Gathering Under Dynamics Uncertainty](https://mlsanity.com/paper/2601.21988/) (2026)
- [An Interpretable Data-Driven Model of the Flight Dynamics of Hawks](https://mlsanity.com/paper/2602.19196/) (2026)

## Abstract (arXiv)

This paper presents an active learning strategy for robotic systems that takes into account task information, enables fast learning, and allows control to be readily synthesized by taking advantage of the Koopman operator representation. We first motivate the use of representing nonlinear systems as linear Koopman operator systems by illustrating the improved model-based control performance with an actuated Van der Pol system. Information-theoretic methods are then applied to the Koopman operator formulation of dynamical systems where we derive a controller for active learning of robot dynamics. The active learning controller is shown to increase the rate of information about the Koopman operator. In addition, our active learning controller can readily incorporate policies built on the Koopman dynamics, enabling the benefits of fast active learning and improved control. Results using a quadcopter illustrate single-execution active learning and stabilization capabilities during free-fall. The results for active learning are extended for automating Koopman observables and we implement our method on real robotic systems.