用神经网络模仿模型预测控制，可保证误差上限并减少数据需求。
Imitation Learning of MPC with Neural Networks: Error Guarantees and Sparsification
- 基于神经网络的Lipschitz性质，推导出逼近误差上界，指导数据集设计。
- 引入基于优化问题敏感性的训练调整，降低数据密度要求。
- 在倒立摆仿真中实现与原控制器接近的闭环行为，适合需安全保证的控制场景。
本文提出一种框架，用于界定采用神经网络的模仿模型预测控制器的近似误差。利用神经网络的Lipschitz特性，推导出一个误差上界，该上界可指导数据集设计，确保近似误差保持在预定范围内。我们讨论如何结合现有鲁棒模型预测控制方法生成数据，从而设计出具有性能保证的稳定神经网络控制器。此外，提出一种基于优化问题敏感性的训练调整策略，依据推导出的误差界，降低了对数据集密度的要求。验证表明，该增强方法提升了网络的预测能力，并降低了Lipschitz常数。在模拟倒立摆问题中，该方法使模仿控制器与原始模型预测控制器的闭环行为更加一致。
原文摘要 · Abstract (English)
This paper presents a framework for bounding the approximation error in imitation model predictive controllers utilizing neural networks. Leveraging the Lipschitz properties of these neural networks, we derive a bound that guides dataset design to ensure the approximation error remains at chosen limits. We discuss how this method can be used to design a stable neural network controller with performance guarantees employing existing robust model predictive control approaches for data generation. Additionally, we introduce a training adjustment, which is based on the sensitivities of the optimization problem and reduces dataset density requirements based on the derived bounds. We verify that the proposed augmentation results in improvements to the network's predictive capabilities and a reduction of the Lipschitz constant. Moreover, on a simulated inverted pendulum problem, we show that the approach results in a closer match of the closed-loop behavior between the imitation and the original model predictive controller.
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