基于自动化镜像下降的自适应控制元学习
Meta-Learning for Adaptive Control with Automated Mirror Descent
AI总结：
针对自适应控制中难以获取非线性特征的问题，本文提出结合元学习与镜像下降自适应律的方法，利用参数空间非欧几里得几何特性，通过元学习获取非线性特征并优化势函数，提升控制性能。
摘要：
自适应控制可在不确定性下实现参数学习与稳定控制，该不确定性通过已知非线性特征线性参数化。然而，获取此类非线性特征通常较困难。为解决这一问题，近期研究将元学习与自适应控制结合，从数据中学习非线性特征。但这些基于元学习的控制方法依赖经典梯度下降自适应律，受限于欧几里得几何。本文提出一种结合元学习与基于镜像下降的自适应律的新方法，镜像下降是梯度下降的流行泛化方法，可利用参数空间潜在的非欧几里得几何特性。在我们的方法中，元学习不仅学习非线性特征，还搜索合适的镜像下降势函数以优化控制性能。通过数值仿真，我们证明了所提方法在不确定动力学下学习高效表示和实时跟踪控制性能的有效性。
英文摘要：
Adaptive control achieves concurrent parameter learning and stable control under uncertainties that are linearly parameterized with known nonlinear features. Nonetheless, it is often difficult to obtain such nonlinear features. To address this difficulty, recent progress has been made in integrating meta-learning with adaptive control to learn such nonlinear features from data. However, these meta-learning-based control methods rely on classical adaptation laws using gradient descent, which is confined to the Euclidean geometry. In this paper, we propose a novel method that combines meta-learning and adaptation laws based on mirror descent, a popular generalization of gradient descent, which takes advantage of the potentially non-Euclidean geometry of the parameter space. In our approach, meta-learning not only learns the nonlinear features but also searches for a suitable mirror-descent potential function that optimizes control performance. Through numerical simulations, we demonstrate the effectiveness of the proposed method in learning efficient representations and real-time tracking control performance under uncertain dynamics.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
