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

Antonio Marino, Claudio Pacchierotti, Paolo Robuffo Giordano

TL;DR

This paper tackles distributed control for multi-agent systems by introducing a continuous-time graph neural network, the Liquid-Graph Time-Constant (LGTC), inspired by Liquid Time Constant networks. It analyzes stability via contraction theory and $\delta$ISS, deriving sufficient conditions and presenting a closed-form approximation (CfGC) that preserves contraction without requiring ODE solving. LGTC achieves higher expressivity and reduces communication by enabling selective feature sharing, demonstrated on a flocking task with variable communication range. Compared with GGNN and GraphODE baselines, LGTC and CfGC show competitive accuracy and robustness across topology and range changes, highlighting practical potential for scalable distributed control.

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 therecent Liquid Time Constant (LTC) network. We analyse itsstability leveraging contraction analysis and propose a closed-form model that preserves the model contraction rate and doesnot require solving an ODE at each iteration. Compared todiscrete models like Graph Gated Neural Networks (GGNNs),the higher expressivity of the proposed model guaranteesremarkable performance while reducing the large amountof communicated variables normally required by GNNs. Weevaluate our model on a distributed multi-agent control casestudy (flocking) taking into account variable communicationrange and scalability under non-instantaneous communication

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

TL;DR

This paper tackles distributed control for multi-agent systems by introducing a continuous-time graph neural network, the Liquid-Graph Time-Constant (LGTC), inspired by Liquid Time Constant networks. It analyzes stability via contraction theory and ISS, deriving sufficient conditions and presenting a closed-form approximation (CfGC) that preserves contraction without requiring ODE solving. LGTC achieves higher expressivity and reduces communication by enabling selective feature sharing, demonstrated on a flocking task with variable communication range. Compared with GGNN and GraphODE baselines, LGTC and CfGC show competitive accuracy and robustness across topology and range changes, highlighting practical potential for scalable distributed control.

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 therecent Liquid Time Constant (LTC) network. We analyse itsstability leveraging contraction analysis and propose a closed-form model that preserves the model contraction rate and doesnot require solving an ODE at each iteration. Compared todiscrete models like Graph Gated Neural Networks (GGNNs),the higher expressivity of the proposed model guaranteesremarkable performance while reducing the large amountof communicated variables normally required by GNNs. Weevaluate our model on a distributed multi-agent control casestudy (flocking) taking into account variable communicationrange and scalability under non-instantaneous communication
Paper Structure (8 sections, 4 theorems, 33 equations, 2 figures)

This paper contains 8 sections, 4 theorems, 33 equations, 2 figures.

Table of Contents

  1. INTRODUCTION
  2. PRELIMINARIES
  3. Graph Neural Network
  4. Gated Graph Neural Network
  5. LIQUID-GRAPH TIME CONSTANT NETWORK
  6. CLOSED-FORM APPROXIMATION
  7. VALIDATION EXAMPLE
  8. CONCLUSIONS

Key Result

Theorem 1

Under Assumptions assumption1 and assumption2, a sufficient condition for the system system to be $\delta$ISS is $\mathcal{A}_{\delta} \leq 1$; where Where $\bar{S}_{I,K}$ is the defined as in eq. eq:definitions

Figures (2)

  • Figure 1: Flocking control: a group of agents (yellow dots) move in order to reach the same velocity and to avoid collision. The leader (red dot) moves in order to reach the target (blue cross) and avoids the collision with the other agents.
  • Figure 2: Flocking and Leader Error for GGNN, LGCT, CfGC and GraphODE, varying the team size N with a communication range of $4$m and a variable communication range with $N=25$.

Theorems & Definitions (8)

  • Theorem 1
  • Remark 1
  • Lemma 1
  • Definition III.1
  • Definition III.2
  • Theorem 2
  • Theorem 3
  • proof