  In this paper, we propose a deep learning based control synthesis framework
for fast and online computation of controllers that guarantees the safety of
general nonlinear control systems with unknown dynamics in the presence of
input constraints. Towards this goal, we propose a framework for simultaneously
learning the unknown system dynamics, which can change with time due to
external disturbances, and an integral control law for trajectory tracking
based on imitation learning. Simultaneously, we learn corresponding safety
certificates, which we refer to as Neural Integral Control Barrier Functions
(Neural ICBF's), that automatically encode both the state and input constraints
into a single scalar-valued function and enable the design of controllers that
can guarantee that the state of the unknown system will never leave a safe
subset of the state space. Finally, we provide numerical simulations that
validate our proposed approach and compare it with classical as well as recent
learning based methods from the relevant literature.
