Manifold-Guided Lyapunov Control with Diffusion Models
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866910384394338304 |
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| author | Mukherjee, Amartya Quartz, Thanin Liu, Jun |
| author_facet | Mukherjee, Amartya Quartz, Thanin Liu, Jun |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_17692 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Manifold-Guided Lyapunov Control with Diffusion Models Mukherjee, Amartya Quartz, Thanin Liu, Jun Computer Vision and Pattern Recognition Machine Learning Differential Geometry Optimization and Control Computation 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. |
| title | Manifold-Guided Lyapunov Control with Diffusion Models |
| topic | Computer Vision and Pattern Recognition Machine Learning Differential Geometry Optimization and Control Computation |
| url | https://arxiv.org/abs/2403.17692 |