Optimal Control Operator Perspective and a Neural Adaptive Spectral Method
Fuente:
arXiv
Guardado en:
| Autores principales: | , , , , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2024
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866912159680692224 |
|---|---|
| author | Feng, Mingquan Chen, Zhijie Huang, Yixin Liu, Yizhou Yan, Junchi |
| author_facet | Feng, Mingquan Chen, Zhijie Huang, Yixin Liu, Yizhou Yan, Junchi |
| contents | Optimal control problems (OCPs) involve finding a control function for a dynamical system such that a cost functional is optimized. It is central to physical systems in both academia and industry. In this paper, we propose a novel instance-solution control operator perspective, which solves OCPs in a one-shot manner without direct dependence on the explicit expression of dynamics or iterative optimization processes. The control operator is implemented by a new neural operator architecture named Neural Adaptive Spectral Method (NASM), a generalization of classical spectral methods. We theoretically validate the perspective and architecture by presenting the approximation error bounds of NASM for the control operator. Experiments on synthetic environments and a real-world dataset verify the effectiveness and efficiency of our approach, including substantial speedup in running time, and high-quality in- and out-of-distribution generalization. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_12469 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Optimal Control Operator Perspective and a Neural Adaptive Spectral Method Feng, Mingquan Chen, Zhijie Huang, Yixin Liu, Yizhou Yan, Junchi Systems and Control Artificial Intelligence Machine Learning Optimization and Control Optimal control problems (OCPs) involve finding a control function for a dynamical system such that a cost functional is optimized. It is central to physical systems in both academia and industry. In this paper, we propose a novel instance-solution control operator perspective, which solves OCPs in a one-shot manner without direct dependence on the explicit expression of dynamics or iterative optimization processes. The control operator is implemented by a new neural operator architecture named Neural Adaptive Spectral Method (NASM), a generalization of classical spectral methods. We theoretically validate the perspective and architecture by presenting the approximation error bounds of NASM for the control operator. Experiments on synthetic environments and a real-world dataset verify the effectiveness and efficiency of our approach, including substantial speedup in running time, and high-quality in- and out-of-distribution generalization. |
| title | Optimal Control Operator Perspective and a Neural Adaptive Spectral Method |
| topic | Systems and Control Artificial Intelligence Machine Learning Optimization and Control |
| url | https://arxiv.org/abs/2412.12469 |