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

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 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.

Hamiltonian Deep Neural Networks Guaranteeing Non-vanishing Gradients by Design

“…In this subsection, we consider utilizing sparse weight matrices to enable distributed implementations of H-DNNs. Sparsity structures in neural networks can also be used to encode prior information on relations among elements when learning graph data [23] or to perform distributed control tasks [24], [25].…”

“…It is therefore important to develop large-scale DNN models for which the training can be distributed between physically separated end devices while guaranteeing satisfactory system-wide predictions. Furthermore, distributed DNN architectures enhance data privacy and fault tolerance [21], facilitate the learning from graph inputs [23] and enable the execution of distributed control tasks [24], [25].…”

Distributed neural network control with dependability guarantees: a compositional port-Hamiltonian approach

“…Unfortunately, these assumptions do not hold for the vast majority of real-world large-scale systems. This fact motivates parametrizing the functions χ i (•), π i (•) as highly nonlinear deep neural networks, even when the dynamics (1) are linear (Gama and Sojoudi, 2021;Yang and Matni, 2021).…”

“…These limitations motivate going beyond linear control and suggest parametrizing highly nonlinear distributed policies through Deep Neural Networks (DNNs). Specifically, the recent works ; Khan et al (2020); Gama and Sojoudi (2021); Yang and Matni (2021) have focused on training Graph Neural Networks (GNNs) that parametrize static and dynamical distributed control policies. These methods achieve remarkable performance in applications such as vehicle flocking and formation flying.…”

Universal Approximation Property of Hamiltonian Deep Neural Networks

“…Related work DNNs have shown promise in designing both static and dynamic distributed control policies for largescale systems. Notably, Graph Neural Networks (GNNs) have achieved impressive performance in applications like vehicle flocking and formation flying [24]- [27] thanks to their inherent scalable structure. However, guaranteeing stability with general GNNs remains challenging, often requiring restrictive assumptions like linear, open-loop stable system dynamics or sufficiently small Lipschitz constants [27].…”