# Communication Topology Co-Design in Graph Recurrent Neural Network Based Distributed Control

arXiv: https://arxiv.org/abs/2104.13868 · HTML: https://mlsanity.com/paper/2104.13868/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 19 of its 32 references that are in the map.
- First posted on arXiv 28 Apr 2021.

## Builds on (most cited first, 19 of 19)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Spectral Networks and Locally Connected Networks on Graphs](https://mlsanity.com/paper/1312.6203/) (2013)
- [Diffusion-Convolutional Neural Networks](https://mlsanity.com/paper/1511.02136/) (2015)
- [Stability Properties of Graph Neural Networks](https://mlsanity.com/paper/1905.04497/) (2019)
- [Convolutional Neural Network Architectures for Signals Supported on Graphs](https://mlsanity.com/paper/1805.00165/) (2018)
- [Learning Decentralized Controllers for Robot Swarms with Graph Neural Networks](https://mlsanity.com/paper/1903.10527/) (2019)
- [On the Sample Complexity of Stability Constrained Imitation Learning](https://mlsanity.com/paper/2102.09161/) (2021)
- [Graph Policy Gradients for Large Scale Robot Control](https://mlsanity.com/paper/1907.03822/) (2019)
- [Graph Neural Networks for Decentralized Controllers](https://mlsanity.com/paper/2003.10280/) (2020)
- [Distributed Linear-Quadratic Control with Graph Neural Networks](https://mlsanity.com/paper/2103.08417/) (2021)
- [On Submodularity and Controllability in Complex Dynamical Networks](https://mlsanity.com/paper/1404.7665/) (2014)
- [Sensor Placement for Optimal Kalman Filtering: Fundamental Limits, Submodularity, and Algorithms](https://mlsanity.com/paper/1509.08146/) (2015)
- [A Convex Parameterization of Robust Recurrent Neural Networks](https://mlsanity.com/paper/2004.05290/) (2020)
- [Design of optimal sparse interconnection graphs for synchronization of oscillator networks](https://mlsanity.com/paper/1302.0449/) (2013)
- [Optimal Sensor and Actuator Placement in Complex Dynamical Networks](https://mlsanity.com/paper/1306.2491/) (2013)
- [Regularization for Design](https://mlsanity.com/paper/1404.1972/) (2014)
- [Communication Delay Co-Design in H2 Distributed Control Using Atomic Norm Minimization](https://mlsanity.com/paper/1404.4911/) (2014)
- [Minimum Cost Constrained Input-Output and Control Configuration Co-Design Problem: A Structural Systems Approach](https://mlsanity.com/paper/1503.02764/) (2015)

## Built on by (most cited first, 7 of 7)

- [Hamiltonian Deep Neural Networks Guaranteeing Non-vanishing Gradients by Design](https://mlsanity.com/paper/2105.13205/) (2021)
- [Distributed neural network control with dependability guarantees: a compositional port-Hamiltonian approach](https://mlsanity.com/paper/2112.09046/) (2021)
- [Space-Time Graph Neural Networks](https://mlsanity.com/paper/2110.02880/) (2021)
- [Robust Graph Neural Networks via Probabilistic Lipschitz Constraints](https://mlsanity.com/paper/2112.07575/) (2021)
- [Neural Port-Hamiltonian Models for Nonlinear Distributed Control: An Unconstrained Parametrization Approach](https://mlsanity.com/paper/2411.10096/) (2024)
- [Graph Neural Network-Based Distributed Optimal Control for Linear Networked Systems: An Online Distributed Training Approach](https://mlsanity.com/paper/2504.06439/) (2025)
- [Joint Trajectory, RIS, and Computation Offloading Optimization via Decentralized Model-Based PPO in Urban Multi-UAV Mobile Edge Computing](https://mlsanity.com/paper/2603.20238/) (2026)

## Abstract (arXiv)

When designing large-scale distributed controllers, the information-sharing constraints between sub-controllers, as defined by a communication topology interconnecting them, are as important as the controller itself. Controllers implemented using dense topologies typically outperform those implemented using sparse topologies, but it is also desirable to minimize the cost of controller deployment. Motivated by the above, we introduce a compact but expressive graph recurrent neural network (GRNN) parameterization of distributed controllers that is well suited for distributed controller and communication topology co-design. Our proposed parameterization enjoys a local and distributed architecture, similar to previous Graph Neural Network (GNN)-based parameterizations, while further naturally allowing for joint optimization of the distributed controller and communication topology needed to implement it. We show that the distributed controller/communication topology co-design task can be posed as an ℓ1-regularized empirical risk minimization problem that can be efficiently solved using stochastic gradient methods. We run extensive simulations to study the performance of GRNN-based distributed controllers and show that (a) they achieve performance comparable to GNN-based controllers while having fewer free parameters, and (b) our method allows for performance/communication density tradeoff curves to be efficiently approximated.