This paper introduces innovative data-driven techniques for estimating the noise distribution and KL divergence bound for distributionally robust optimal control (DROC). The proposed approach addresses the limitation of traditional DROC approaches that require known ambiguity sets for the noise distribution, our approach can learn these distributions and bounds in real-world scenarios where they may not be known a priori. To evaluate the effectiveness of our approach, a navigation problem involving a car-like robot under different noise distributions is used as a numerical example. The results demonstrate that DROC combined with the proposed data-driven approaches, what we call D3ROC, provide robust and efficient control policies that outperform the traditional iterative linear quadratic Gaussian (iLQG) control approach. Moreover, it shows the effectiveness of our proposed approach in handling different noise distributions. Overall, the proposed approach offers a promising solution to real-world DROC problems where the noise distribution and KL divergence bounds may not be known a priori, increasing the practicality and applicability of the DROC framework.

翻译：本文提出了一种创新的数据驱动技术，用于估计分布鲁棒最优控制（DROC）中的噪声分布及KL散度界。所提方法克服了传统DROC方法需预先已知噪声分布模糊集的局限性，能够从实际场景中学习这些分布及其界（而无需先验知识）。为评估方法的有效性，以包含不同噪声分布的类车机器人导航问题作为数值算例。结果表明，结合所提数据驱动方法（命名为D3ROC）的DROC策略，能提供比传统迭代线性二次高斯（iLQG）控制方法更鲁棒且更高效的控制策略。此外，该方法在处理不同噪声分布时展现出显著有效性。总体而言，所提方法为噪声分布及KL散度界未知的实际DROC问题提供了有前景的解决方案，提升了DROC框架的实用性与适用性。