Manifold-Guided Lyapunov Control with Diffusion Models
<|reference_start|>Manifold-Guided Lyapunov Control with Diffusion Models: 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.<|reference_end|>
@article{mukherjee2024manifold-guided,
    title={Manifold-Guided Lyapunov Control with Diffusion Models},
    author={Amartya Mukherjee, Thanin Quartz, Jun Liu},
    journal={arXiv preprint arXiv:2403.17692},
    year={2024},
    archivePrefix={arXiv},
    eprint={2403.17692},
    primaryClass={cs.CV cs.LG math.DG math.OC stat.CO}
}