Optimal control problems (OCPs) are mathematical problems that involve finding a control policy for a dynamical system to optimize a certain performance criterion. These problems are central to many applications in engineering and science, where the goal is to control a system in the most efficient way possible. The Neural Adaptive Spectral Method (NASM) is a novel approach to solving OCPs, leveraging neural networks to approximate the control operator. This method generalizes classical spectral methods, which are used to solve differential equations by transforming them into a frequency domain. NASM offers a one-shot solution to OCPs, meaning it can find the optimal control policy without iterative optimization processes. This is achieved by implementing a neural operator architecture that approximates the control operator, validated by theoretical error bounds. The method is tested on synthetic and real-world datasets, demonstrating its effectiveness in providing high-quality solutions with substantial speedup in running time. NASM represents a significant advancement in the field of optimal control, offering a powerful tool for both academic research and industrial applications.
Neural Adaptive Spectral Method
Neural operator architecture
Synthetic and real-world datasets
Approximation error bounds
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One-shot solution to OCPs, high-quality solutions, speedup in running time
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No
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Engineering, Science
Optimal control problems
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No
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No
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No
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0.00
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01/01/1970
01/01/1970
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Yes