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

TL;DR

This paper introduces a graph recurrent neural network (GRNN) approach for co-designing distributed controllers and communication topologies, enabling efficient optimization and performance tradeoffs in large-scale distributed control systems.

Contribution

It proposes a novel GRNN parameterization that facilitates joint optimization of controllers and communication topologies, improving efficiency and performance in distributed control design.

Findings

GRNN controllers achieve comparable performance to existing GNN controllers with fewer parameters.

The method efficiently approximates performance versus communication density tradeoff curves.

Joint optimization via -regularized empirical risk minimization is effective for topology and controller co-design.

Abstract

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 $\ell_1$-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.