Input State Stability of Gated Graph Neural Networks

In this article, we aim to find the conditions for the input-to-state stability (ISS) and incremental ISS of gated graph neural networks (GGNNs). We show that this recurrent version of graph neural networks can be expressed as a dynamical distributed system and, as a consequence, can be analyzed using model-based techniques to assess its stability and robustness properties. Then, the stability criteria found can be exploited as constraints during the training process to enforce the internal stability of the neural network. Two distributed control examples, i.e., flocking and multirobot motion control, show that using these conditions increases the performance and robustness of the GGNNs.