Meta-Learning for Adaptive Control with Automated Mirror Descent

TL;DR

This paper introduces a novel meta-learning adaptive control method that employs mirror descent to better handle non-Euclidean parameter spaces, improving real-time control under uncertainties.

Contribution

It combines meta-learning with mirror descent adaptation laws, enabling learning of nonlinear features and suitable geometries for enhanced control performance.

Findings

Effective learning of nonlinear features from data.

Improved real-time tracking control under uncertainties.

Demonstrated advantages over classical gradient-based methods.

Abstract

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.