Lyapunov-Based Graph Neural Networks for Adaptive Control of Multi-Agent Systems
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| Main Authors: | , , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866915205287510016 |
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| author | Fallin, Brandon C. Nino, Cristian F. Patil, Omkar Sudhir Bell, Zachary I. Dixon, Warren E. |
| author_facet | Fallin, Brandon C. Nino, Cristian F. Patil, Omkar Sudhir Bell, Zachary I. Dixon, Warren E. |
| contents | Graph neural networks (GNNs) have a message-passing framework in which vector messages are exchanged between graph nodes and updated using feedforward layers. The inclusion of distributed message-passing in the GNN architecture makes them ideally suited for distributed control and coordination tasks. Existing results develop GNN-based controllers to address a variety of multi-agent control problems while compensating for modeling uncertainties in the systems. However, these results use GNNs that are pre-trained offline. This paper provides the first result on GNNs with stability-driven online weight updates to address the multi-agent target tracking problem. Specifically, new Lyapunov-based distributed GNN and graph attention network (GAT)-based controllers are developed to adaptively estimate unknown target dynamics and address the second-order target tracking problem. A Lyapunov-based stability analysis is provided to guarantee exponential convergence of the target state estimates and agent states to a neighborhood of the target state. Numerical simulations show a 20.8% and 48.1% position tracking error performance improvement by the GNN and GAT architectures over a baseline DNN architecture, respectively. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_15360 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Lyapunov-Based Graph Neural Networks for Adaptive Control of Multi-Agent Systems Fallin, Brandon C. Nino, Cristian F. Patil, Omkar Sudhir Bell, Zachary I. Dixon, Warren E. Systems and Control Graph neural networks (GNNs) have a message-passing framework in which vector messages are exchanged between graph nodes and updated using feedforward layers. The inclusion of distributed message-passing in the GNN architecture makes them ideally suited for distributed control and coordination tasks. Existing results develop GNN-based controllers to address a variety of multi-agent control problems while compensating for modeling uncertainties in the systems. However, these results use GNNs that are pre-trained offline. This paper provides the first result on GNNs with stability-driven online weight updates to address the multi-agent target tracking problem. Specifically, new Lyapunov-based distributed GNN and graph attention network (GAT)-based controllers are developed to adaptively estimate unknown target dynamics and address the second-order target tracking problem. A Lyapunov-based stability analysis is provided to guarantee exponential convergence of the target state estimates and agent states to a neighborhood of the target state. Numerical simulations show a 20.8% and 48.1% position tracking error performance improvement by the GNN and GAT architectures over a baseline DNN architecture, respectively. |
| title | Lyapunov-Based Graph Neural Networks for Adaptive Control of Multi-Agent Systems |
| topic | Systems and Control |
| url | https://arxiv.org/abs/2503.15360 |