# Computationally Efficient Data-Driven Discovery and Linear Representation of Nonlinear Systems For Control

arXiv: https://arxiv.org/abs/2309.04074 · HTML: https://mlsanity.com/paper/2309.04074/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 8 of its 19 references that are in the map.
- First posted on arXiv 8 Sep 2023.

## Builds on (most cited first, 8 of 8)

- [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)
- [Linear predictors for nonlinear dynamical systems: Koopman operator meets model predictive control](https://mlsanity.com/paper/1611.03537/) (2016)
- [Extended Dynamic Mode Decomposition with Learned Koopman Eigenfunctions for Prediction and Control](https://mlsanity.com/paper/1911.08751/) (2019)
- [Deep Neural Networks with Koopman Operators for Modeling and Control of Autonomous Vehicles](https://mlsanity.com/paper/2007.02219/) (2020)
- [Neural Koopman Lyapunov Control](https://mlsanity.com/paper/2201.05098/) (2022)
- [Data-Driven Models for Control Engineering Applications Using the Koopman Operator](https://mlsanity.com/paper/2112.07983/) (2021)
- [Vehicular Applications of Koopman Operator Theory -- A Survey](https://mlsanity.com/paper/2303.10471/) (2023)

## Built on by (most cited first, 4 of 4)

- [Leveraging KANs For Enhanced Deep Koopman Operator Discovery](https://mlsanity.com/paper/2406.02875/) (2024)
- [SafEDMD: A Koopman-based data-driven controller design framework for nonlinear dynamical systems](https://mlsanity.com/paper/2402.03145/) (2024)
- [Deep Learning Based Dynamics Identification and Linearization of Orbital Problems using Koopman Theory](https://mlsanity.com/paper/2403.08965/) (2024)
- [End-to-end guarantees for indirect data-driven control of bilinear systems with finite stochastic data](https://mlsanity.com/paper/2409.18010/) (2024)

## Abstract (arXiv)

This work focuses on developing a data-driven framework using Koopman operator theory for system identification and linearization of nonlinear systems for control. Our proposed method presents a deep learning framework with recursive learning. The resulting linear system is controlled using a linear quadratic control. An illustrative example using a pendulum system is presented with simulations on noisy data. We show that our proposed method is trained more efficiently and is more accurate than an autoencoder baseline.