  Modern control systems routinely employ wireless networks to exchange
information between spatially distributed plants, actuators and sensors. With
wireless networks defined by random, rapidly changing transmission conditions
that challenge assumptions commonly held in the design of control systems,
proper allocation of communication resources is essential to achieve reliable
operation. Designing resource allocation policies, however, is challenging,
motivating recent works to successfully exploit deep learning and deep
reinforcement learning techniques to design resource allocation and scheduling
policies for wireless control systems (WCSs). As the number of learnable
parameters in a neural network grows with the size of the input signal, deep
reinforcement learning may fail to scale, limiting the immediate generalization
of such scheduling and resource allocation policies to large-scale systems. The
interference and fading patterns among plants and controllers in the network,
however, induce a time-varying graph that can be used to construct policy
representations based on graph neural networks (GNNs), with the number of
learnable parameters now independent of the number of plants in the network. We
further establish in the context of WCSs that, due to inherent invariance to
graph permutations, the GNN is able to model scalable and transferable resource
allocation policies, which are subsequently trained with primal-dual
reinforcement learning. Numerical experiments show that the proposed graph
reinforcement learning approach yields policies that not only outperform
baseline solutions and deep reinforcement learning based policies in
large-scale systems, but that can also be transferred across networks of
varying size.
