Optimal Control Operator Perspective and a Neural Adaptive Spectral Method

• URL: http://arxiv.org/abs/2412.12469v1
• Date: Tue, 17 Dec 2024 02:06:34 GMT
• Title: Optimal Control Operator Perspective and a Neural Adaptive Spectral Method
• Authors: Mingquan Feng, Zhijie Chen, Yixin Huang, Yizhou Liu, Junchi Yan,
• Abstract summary: Optimal control problems (OCPs) involve finding a control function for a dynamical system such that a cost functional is optimized. We propose a novel instance-solution control operator perspective, which solves OCPs in a one-shot manner. Experiments on synthetic environments and a real-world dataset verify the effectiveness and efficiency of our approach.
• Score: 43.684201849848314
• License:
• 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.

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