  Learn-to-Fly (L2F) is a new framework that aims to replace the traditional
iterative development paradigm for aerial vehicles with a combination of
real-time aerodynamic modeling, guidance, and learning control. To ensure safe
learning of the vehicle dynamics on the fly, this paper presents an
$\mathcal{L}_1$ adaptive control ($\mathcal{L}_1$AC) based scheme, which
actively estimates and compensates for the discrepancy between the
intermediately learned dynamics and the actual dynamics. First, to incorporate
the periodic update of the learned model within the L2F framework, this paper
extends the $\mathcal{L}_1$AC architecture to handle a switched reference
system subject to unknown time-varying parameters and disturbances. The paper
also includes an analysis of both transient and steady-state performance of the
$\mathcal{L}_1$AC architecture in the presence of non-zero initialization error
for the state predictor. Second, the paper presents how the proposed
$\mathcal{L}_1$AC scheme is integrated into the L2F framework, including its
interaction with the baseline controller and the real-time modeling module.
Finally, flight tests on an unmanned aerial vehicle (UAV) validate the efficacy
of the proposed control and learning scheme.
