Optimal Control Operator Perspective and a Neural Adaptive Spectral Method
Mingquan Feng, Zhijie Chen, Yixin Huang, Yizhou Liu, Junchi Yan
Abstract
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.
BibTeX
@article{Feng_Chen_Huang_Liu_Yan_2025, title={Optimal Control Operator Perspective and a Neural Adaptive Spectral Method}, volume={39}, url={https://ojs.aaai.org/index.php/AAAI/article/view/33596}, DOI={10.1609/aaai.v39i14.33596}, abstractNote={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.}, number={14}, journal={Proceedings of the AAAI Conference on Artificial Intelligence}, author={Feng, Mingquan and Chen, Zhijie and Huang, Yixin and Liu, Yizhou and Yan, Junchi}, year={2025}, month={Apr.}, pages={14567-14575} }