# Distributed Linear-Quadratic Control with Graph Neural Networks

arXiv: https://arxiv.org/abs/2103.08417 · HTML: https://mlsanity.com/paper/2103.08417/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 15 Mar 2021.

## Built on by (most cited first, 12 of 12)

- [Learning by Transference: Training Graph Neural Networks on Growing Graphs](https://mlsanity.com/paper/2106.03693/) (2021)
- [Hamiltonian Deep Neural Networks Guaranteeing Non-vanishing Gradients by Design](https://mlsanity.com/paper/2105.13205/) (2021)
- [Wide and Deep Graph Neural Network with Distributed Online Learning](https://mlsanity.com/paper/2107.09203/) (2021)
- [Space-Time Graph Neural Networks](https://mlsanity.com/paper/2110.02880/) (2021)
- [Unsupervised Learning of Sampling Distributions for Particle Filters](https://mlsanity.com/paper/2302.01174/) (2023)
- [Communication Topology Co-Design in Graph Recurrent Neural Network Based Distributed Control](https://mlsanity.com/paper/2104.13868/) (2021)
- [Node-Variant Graph Filters in Graph Neural Networks](https://mlsanity.com/paper/2106.00089/) (2021)
- [Scalable Perception-Action-Communication Loops with Convolutional and Graph Neural Networks](https://mlsanity.com/paper/2106.13358/) (2021)
- [Promoting Fairness in GNNs: A Characterization of Stability](https://mlsanity.com/paper/2309.03648/) (2023)
- [Graph Neural Network-Based Distributed Optimal Control for Linear Networked Systems: An Online Distributed Training Approach](https://mlsanity.com/paper/2504.06439/) (2025)
- [Distributed Control of Network Systems in the Space of Stabilizing Graph Neural Network Policies](https://mlsanity.com/paper/2512.18540/) (2025)
- [Model-Based and Data-Driven Hierarchical Control and Topology Co-Design for Robust Networked Systems](https://mlsanity.com/paper/2606.11596/) (2026)

## Abstract (arXiv)

Controlling network systems has become a problem of paramount importance. In this paper, we consider a distributed linear-quadratic problem and propose the use of graph neural networks (GNNs) to parametrize and design a distributed controller for network systems. GNNs exhibit many desirable properties, such as being naturally distributed and scalable. We cast the distributed linear-quadratic problem as a self-supervised learning problem, which is then used to train the GNN-based controllers. We also obtain sufficient conditions for the resulting closed-loop system to be input-state stable, and derive an upper bound on how much the trajectory deviates from the nominal value when the matrices that describe the system are not accurately known. We run extensive simulations to study the performance of GNN-based distributed controllers and show that they are computationally efficient and scalable.