  Modeling of nonlinear behaviors with physical-based models poses challenges.
However, Koopman operator maps the original nonlinear system into an
infinite-dimensional linear space to achieve global linearization of the
nonlinear system through input and output data, which derives an absolute
equivalent linear representation of the original state space. Due to the
impossibility of implementing the infinite-dimensional Koopman operator,
finite-dimensional kernel functions are selected as an approximation. Given its
flexible structure and high accuracy, deep learning is initially employed to
extract kernel functions from data and acquire a linear evolution dynamic of
the autonomous vehicle in the lifted space. Additionally, the control barrier
function (CBF) converts the state constraints to the constraints on the input
to render safety property. Then, in terms of the lateral stability of the
in-wheel motor driven vehicle, the CBF conditions are incorporated with the
learned deep Koopman model. Because of the linear fashion of the deep Koopman
model, the quadratic programming problem is formulated to generate the applied
driving torque with minimal perturbation to the original driving torque as a
safety command governor. In the end, to validate the fidelity of the deep
Koopman model compared to other mainstream approaches and demonstrate the
lateral improvement achieved by the proposed safety command governor, data
collection and safety testing scenarios are conducted on a hardware-in-the-loop
platform.
