  We address the problem of stable and robust control of vehicles with lateral
error dynamics for the application of lane keeping. Lane departure is the
primary reason for half of the fatalities in road accidents, making the
development of stable, adaptive and robust controllers a necessity. Traditional
linear feedback controllers achieve satisfactory tracking performance, however,
they exhibit unstable behavior when uncertainties are induced into the system.
Any disturbance or uncertainty introduced to the steering-angle input can be
catastrophic for the vehicle. Therefore, controllers must be developed to
actively handle such uncertainties. In this work, we introduce a Neural L1
Adaptive controller (Neural-L1) which learns the uncertainties in the lateral
error dynamics of a front-steered Ackermann vehicle and guarantees stability
and robustness. Our contributions are threefold: i) We extend the theoretical
results for guaranteed stability and robustness of conventional L1 Adaptive
controllers to Neural-L1; ii) We implement a Neural-L1 for the lane keeping
application which learns uncertainties in the dynamics accurately; iii)We
evaluate the performance of Neural-L1 on a physics-based simulator, PyBullet,
and conduct extensive real-world experiments with the F1TENTH platform to
demonstrate superior reference trajectory tracking performance of Neural-L1
compared to other state-of-the-art controllers, in the presence of
uncertainties. Our project page, including supplementary material and videos,
can be found at https://mukhe027.github.io/Neural-Adaptive-Control/
