Scalable Formal Verification of Incremental Stability in Large-Scale Systems Using Graph Neural Networks

Abstract

This work proposes a novel distributed framework for verifying the incremental stability of large-scale systems with unknown dynamics and known interconnection structures using graph neural networks. Our proposed approach relies on the construction of local incremental Lyapunov functions for subsystems, which are then composed together to obtain a suitable Lyapunov function for the interconnected system. Graph neural networks are used to synthesize these functions in a data-driven fashion. The formal correctness guarantee is then obtained by leveraging Lipschitz bounds of the trained neural networks. Finally, the effectiveness of our approach is validated through two nonlinear case studies.