# Data-Driven Linear Koopman Embedding for Networked Systems: Model-Predictive Grid Control

arXiv: https://arxiv.org/abs/2206.01272 · HTML: https://mlsanity.com/paper/2206.01272/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 53 references that are in the map.
- First posted on arXiv 2 Jun 2022.

## Builds on (most cited first, 12 of 12)

- [Deep learning for universal linear embeddings of nonlinear dynamics](https://mlsanity.com/paper/1712.09707/) (2017)
- [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)
- [Safety Verification and Robustness Analysis of Neural Networks via Quadratic Constraints and Semidefinite Programming](https://mlsanity.com/paper/1903.01287/) (2019)
- [Reinforcement Learning for Selective Key Applications in Power Systems: Recent Advances and Future Challenges](https://mlsanity.com/paper/2102.01168/) (2021)
- [Formulas for Data-driven Control: Stabilization, Optimality and Robustness](https://mlsanity.com/paper/1903.06842/) (2019)
- [Adaptive Power System Emergency Control using Deep Reinforcement Learning](https://mlsanity.com/paper/1903.03712/) (2019)
- [Deep Learning of Koopman Representation for Control](https://mlsanity.com/paper/2010.07546/) (2020)
- [Deep Koopman Operator with Control for Nonlinear Systems](https://mlsanity.com/paper/2202.08004/) (2022)
- [Deep Neural Networks with Koopman Operators for Modeling and Control of Autonomous Vehicles](https://mlsanity.com/paper/2007.02219/) (2020)
- [Power grid transient stabilization using Koopman model predictive control](https://mlsanity.com/paper/1803.10744/) (2018)
- [Data-driven Identification of Nonlinear Power System Dynamics Using Output-only Measurements](https://mlsanity.com/paper/2110.01469/) (2021)

## Built on by (most cited first, 2 of 2)

- [Learning the Causal Structure of Networked Dynamical Systems under Latent Nodes and Structured Noise](https://mlsanity.com/paper/2312.05974/) (2023)
- [NeuroKoopman Dynamic Causal Discovery](https://mlsanity.com/paper/2404.16326/) (2024)

## Abstract (arXiv)

This paper presents a data-learned linear Koopman embedding of nonlinear networked dynamics and uses it to enable real-time model predictive emergency voltage control in a power network. The approach involves a novel data-driven ``basis-dictionary free" lifting of the system dynamics into a higher dimensional linear space over which an MPC (model predictive control) is exercised, making it both scalable and rapid for practical real-time implementation. A Koopman-inspired deep neural network (KDNN) encoder-decoder architecture for the linear embedding of the underlying dynamics under distributed controls is presented, in which the end-to-end components of the KDNN comprising of a triple of transforms is learned from the system trajectory data in one go: A Neural Network (NN)-based lifting to a higher dimension, a linear dynamics within that higher dimension, and an NN-based projection to the original space. This data-learned approach relieves the burden of the ad-hoc selection of the nonlinear basis functions (e.g., polynomial or radial) used in conventional approaches for lifting to higher dimensional linear space. We validate the efficacy and robustness of the approach via application to the standard IEEE 39-bus system.