Contraction $\mathcal{L}_1$-Adaptive Control using Gaussian Processes
This work addresses safety and optimality in control systems with uncertainties, particularly for applications like planar quadrotors, but it appears incremental as it integrates existing methods.
The paper tackles the problem of safe simultaneous learning and control for uncertain systems by introducing a framework that combines contraction theory-based control with Gaussian process regression, ensuring safety during learning transients and improving performance through data incorporation.
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.