GNN-Based Distributed Consensus Control for Heterogeneous Multi-Agent Systems with Linear and Fully Actuated Nonlinear Model

This paper proposes a novel Graph Neural Network (GNN)-based distributed consensus control strategy for heterogeneous multi-agent systems (MAS) with both linear dynamics and high-order fully actuated nonlinear dynamics. Traditional methods often struggle to optimize quadratic objectives in distributed consensus controller design, especially in heterogeneous MAS where agent dynamics and input dimensions vary. To address this challenge, we introduce a GNN-based approach that directly learns a nonlinear distributed consensus control policy by optimizing a finite-horizon linear quadratic regulator (LQR) objective. By leveraging the inherently distributed architecture of GNNs, the proposed method enables each agent to reach consensus using only local information from its neighbors, while maintaining scalability across diverse network topologies. Simulation results under various stability conditions validate the controller's effectiveness and demonstrate superior quadratic performance compared to conventional linear consensus methods.