Optimal Control Operator Perspective and a Neural Adaptive Spectral Method

作     者：Feng, Mingquan Chen, Zhijie Huang, Yixin Liu, Yizhou Yan, Junchi 

作者机构：School of Electronic Information & Electrical Engineering Shanghai Jiao Tong University Shanghai China Siebel School of Computing and Data Science University of Illinois at Urbana-Champaign UrbanaIL United States School of Artificial Intelligence MoE Lab of AI Shanghai Jiao Tong University Shanghai China 

出 版 物：《arXiv》 (arXiv)

年 卷 期：2024年

核心收录：

主　　题：Optimal control systems 

摘      要：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. © 2024, CC BY-NC-ND.