Distributed Control of Network Systems in the Space of Stabilizing Graph Neural Network Policies

2025/12/20 by John Cao, Cao, John, Luca Furieri +1
Computer Science · #Adaptive Dynamic Programming Control #Advanced Graph Neural Networks #FOS: Computer and information sciences #FOS: Electrical engineering #FOS: Mathematics #Machine Learning (cs.LG) #Optimization and Control (math.OC) #Reinforcement Learning in Robotics #Systems and Control (eess.SY) #electronic engineering #information engineering

paper · doi:10.48550/arxiv.2512.18540

openalex publication_date 2025/12/20 · openalex created_date 2025/12/24 · openalex updated_date 2026/07/28

Abstract

We study distributed control of networked systems through reinforcement learning, where neural policies must be simultaneously scalable, expressive and stabilizing. We introduce a policy parameterization that embeds Graph Neural Networks (GNNs) into a Youla-like magnitude-direction parameterization, yielding distributed stochastic controllers that guarantee network-level closed-loop stability by design. The magnitude is implemented as a stable operator consisting of a GNN acting on disturbance feedback, while the direction is a GNN acting on local observations. We prove robustness of the policy to perturbations in both the graph topology and model parameters. Numerical experiments validate the effectiveness of the proposed approach.

Citations

• MAD: A Magnitude And Direction Policy Parametrization for Stability Constrained Reinforcement Learning
• Optimal distributed control with stability guarantees by training a network of neural closed-loop maps
• On Safety and Liveness Filtering Using Hamilton-Jacobi Reachability Analysis
• Scalable Multi-Agent Reinforcement Learning through Intelligent Information Aggregation
• KCRL: Krasovskii-Constrained Reinforcement Learning with Guaranteed Stability in Nonlinear Dynamical Systems
• Neural System Level Synthesis: Learning over All Stabilizing Policies for Nonlinear Systems
• Distributed neural network control with dependability guarantees: a compositional port-Hamiltonian approach
• Learning over All Stabilizing Nonlinear Controllers for a Partially-Observed Linear System
• Distributed Linear-Quadratic Control with Graph Neural Networks
• Masked Label Prediction: Unified Message Passing Model for Semi-Supervised Classification
• Global Convergence of Policy Gradient Methods for the Linear Quadratic Regulator
• Proximal Policy Optimization Algorithms
• Semi-Supervised Classification with Graph Convolutional Networks
• Finding Structure in Time

Related

• Graph Reinforcement Learning for Network Control via Bi-Level Optimization
• Optimal distributed control with stability guarantees by training a network of neural closed-loop maps
• Scalable Policy Optimization for Networked Multi-Agent Reinforcement Learning with Continuous State-Action Spaces
• Distributed Linear-Quadratic Control with Graph Neural Networks
• Graph Neural Networks for Distributed Linear-Quadratic Control