Collaborative Indirect Influencing and Control on Graphs using Graph Neural Networks

TL;DR

This paper introduces a GNN-based control method for networked systems that enables cooperative nodes to regulate uncertain target dynamics in real time, with proven stability and demonstrated effectiveness.

Contribution

It proposes a novel GNN-based backstepping control strategy with formal stability guarantees for indirect influence in networked systems.

Findings

Successful real-time regulation of uncertain target dynamics

Formal stability guarantees established via Lyapunov analysis

Numerical simulations confirm control performance

Abstract

This paper presents a novel approach to solving the indirect influence problem in networked systems, in which cooperative nodes must regulate a target node with uncertain dynamics to follow a desired trajectory. We leverage the message-passing structure of a graph neural network (GNN), allowing nodes to collectively learn the unknown target dynamics in real time. We develop a novel GNN-based backstepping control strategy with formal stability guarantees derived from a Lyapunov-based analysis. Numerical simulations are included to demonstrate the performance of the developed controller.