  Autonomous driving technologies have received notable attention in the past
decades. In autonomous driving systems, identifying a precise dynamical model
for motion control is nontrivial due to the strong nonlinearity and uncertainty
in vehicle dynamics. Recent efforts have resorted to machine learning
techniques for building vehicle dynamical models, but the generalization
ability and interpretability of existing methods still need to be improved. In
this paper, we propose a data-driven vehicle modeling approach based on deep
neural networks with an interpretable Koopman operator. The main advantage of
using the Koopman operator is to represent the nonlinear dynamics in a linear
lifted feature space. In the proposed approach, a deep learning-based extended
dynamic mode decomposition algorithm is presented to learn a finite-dimensional
approximation of the Koopman operator. Furthermore, a data-driven model
predictive controller with the learned Koopman model is designed for path
tracking control of autonomous vehicles. Simulation results in a high-fidelity
CarSim environment show that our approach exhibit a high modeling precision at
a wide operating range and outperforms previously developed methods in terms of
modeling performance. Path tracking tests of the autonomous vehicle are also
performed in the CarSim environment and the results show the effectiveness of
the proposed approach.
