Contraction $\mathcal{L}_1$-Adaptive Control using Gaussian Processes

TL;DR

This paper introduces a control framework combining contraction theory-based $ ext{L}_1$ control with Gaussian process regression to enable safe, adaptive learning and control of uncertain systems, demonstrated on quadrotors.

Contribution

The novel integration of $ ext{L}_1$ control with Gaussian processes for safe adaptive control and learning in uncertain systems.

Findings

Ensures safety during learning transients.

Improves control performance with data-driven uncertainty modeling.

Validates approach on planar quadrotor systems.

Abstract

We present $\mathcal{CL}_1$-$\mathcal{GP}$, a control framework that enables safe simultaneous learning and control for systems subject to uncertainties. The two main constituents are contraction theory-based $\mathcal{L}_1$ ($\mathcal{CL}_1$) control and Bayesian learning in the form of Gaussian process (GP) regression. The $\mathcal{CL}_1$ controller ensures that control objectives are met while providing safety certificates. Furthermore, $\mathcal{CL}_1$-$\mathcal{GP}$ incorporates any available data into a GP model of uncertainties, which improves performance and enables the motion planner to achieve optimality safely. This way, the safe operation of the system is always guaranteed, even during the learning transients. We provide a few illustrative examples for the safe learning and control of planar quadrotor systems in a variety of environments.