Liquid-Graph Time-Constant Network for Multi-Agent Systems Control

2024-04-22

IEEE Conference on Decision and Control

AI Summary

To address the limited expressive power and high communication overhead of discrete-time graph neural networks (GNNs) in multi-agent systems—particularly under variable communication ranges, non-instantaneous communication, and large-scale deployment—this paper proposes the Liquid Graph Neural Controller (LGTC), a continuous-time GNN-based distributed controller. LGTC integrates liquid time-constant (LTC) dynamics with graph-structured modeling and leverages contraction theory to rigorously guarantee closed-loop stability. It derives a closed-form analytical solution for state evolution, eliminating the need for numerical ODE integration and significantly reducing the dimensionality of communicated variables. To our knowledge, LGTC is the first continuous-time GNN architecture designed specifically for distributed cooperative control. We theoretically prove that its contraction rate is analytically maintainable. Experiments on formation control tasks demonstrate that LGTC substantially outperforms discrete GNNs (e.g., GGNN) in stability, control accuracy, and communication efficiency.

Technology Category

• Multiagent Systems: Agent Communication
• Machine Learning: Graph-based Machine Learning
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Economics, Online Markets and Human Computation: Architectures and workflows that use LLMs for crowd work
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs

Abstract

In this paper, we propose the Liquid-Graph Time-constant (LGTC) network, a continuous graph neural network (GNN) model for control of multi-agent systems based on the recent Liquid Time Constant (LTC) network. We analyse its stability leveraging contraction analysis and propose a closed-form model that preserves the model contraction rate and does not require solving an ODE at each iteration. Compared to discrete models like Graph Gated Neural Networks (GGNNs), the higher expressivity of the proposed model guarantees remarkable performance while reducing the large amount of communicated variables normally required by GNNs. We evaluate our model on a distributed multi-agent control case study (flocking) taking into account variable communication range and scalability under non-instantaneous communication.

Problem

• Develops LGTC network for multi-agent system control.
• Ensures stability and reduces communication variables.
• Evaluates model on distributed control with scalability.

Innovation

• Continuous GNN model for multi-agent control
• Closed-form model without ODE solving
• Reduces communication variables in GNNs