  Dynamical systems consisting of a set of autonomous agents face the challenge
of having to accomplish a global task, relying only on local information. While
centralized controllers are readily available, they face limitations in terms
of scalability and implementation, as they do not respect the distributed
information structure imposed by the network system of agents. Given the
difficulties in finding optimal decentralized controllers, we propose a novel
framework using graph neural networks (GNNs) to \emph{learn} these controllers.
GNNs are well-suited for the task since they are naturally distributed
architectures and exhibit good scalability and transferability properties. We
show that GNNs learn appropriate decentralized controllers by means of
imitation learning, leverage their permutation invariance properties to
successfully scale to larger teams and transfer to unseen scenarios at
deployment time. The problems of flocking and multi-agent path planning are
explored to illustrate the potential of GNNs in learning decentralized
controllers.
