Distributed Linear-Quadratic Control with Graph Neural Networks

TL;DR

This paper introduces a novel approach using graph neural networks to design distributed controllers for network systems, ensuring stability and robustness, and demonstrating scalability through extensive simulations.

Contribution

It proposes a GNN-based framework for distributed linear-quadratic control, including stability conditions and robustness bounds, which is a new application of GNNs in control design.

Findings

GNN controllers are computationally efficient and scalable.

The method guarantees input-state stability under certain conditions.

Simulations confirm the effectiveness of GNN-based controllers.

Abstract

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.