  This paper proposes a novel extension of the Simplex architecture with model
switching and model learning to achieve safe velocity regulation of
self-driving vehicles in dynamic and unforeseen environments. To guarantee the
reliability of autonomous vehicles, an $\mathcal{L}_{1}$ adaptive controller
that compensates for uncertainties and disturbances is employed by the Simplex
architecture as a verified safe controller to tolerate concurrent software and
physical failures. Meanwhile, safe switching controller is incorporated into
the Simplex for safe velocity regulation through the integration of the
traction control system and anti-lock braking system. Specifically, the
vehicle's angular and longitudinal velocities asymptotically track the provided
references that vary with driving environments, while the wheel slips are
restricted to safety envelopes to prevent slipping and sliding. Due to the high
dependence of vehicle dynamics on the driving environments, the proposed
Simplex leverages the finite-time model learning to timely learn and update the
vehicle model for $\mathcal{L}_{1}$ adaptive controller, when any deviation
from the safety envelope or the uncertainty measurement threshold occurs in the
unforeseen driving environments. Finally, the effectiveness of the proposed
Simplex architecture for safe velocity regulation is validated by the AutoRally
platform.
