Manifold-Guided Lyapunov Control with Diffusion Models
This addresses the challenge of fast zero-shot control for dynamical systems, though it appears incremental as it applies diffusion models to an existing control framework.
The paper tackles the problem of generating stabilizing controllers for dynamical systems by using diffusion models to identify the closest asymptotically stable vector field relative to a predetermined manifold and adjusting control functions accordingly, achieving efficient and rapid stabilization over unseen systems.
This paper presents a novel approach to generating stabilizing controllers for a large class of dynamical systems using diffusion models. The core objective is to develop stabilizing control functions by identifying the closest asymptotically stable vector field relative to a predetermined manifold and adjusting the control function based on this finding. To achieve this, we employ a diffusion model trained on pairs consisting of asymptotically stable vector fields and their corresponding Lyapunov functions. Our numerical results demonstrate that this pre-trained model can achieve stabilization over previously unseen systems efficiently and rapidly, showcasing the potential of our approach in fast zero-shot control and generalizability.