Analytical Lyapunov Function Discovery: An RL-based Generative Approach

We propose an end-to-end framework using transformers to construct analytical (local) Lyapunov functions for addressing key challenges in current neural networkbased approaches, namely scalability and interpretability. Our framework includes a transformer-based generator, which proposes candidate Lyapunov functions, and a falsifier that validates these candidates. The model is updated via risk-seeking policy gradient. We demonstrate the efficiency of our approach on a range of nonlinear dynamical systems with up to ten dimensions and show that it can discover Lyapunov functions not previously identified in the control literature. This work has been accepted by International Conference on Machine Learning 2025. Full implementation is available on Github.