Deep Neural Networks With Koopman Operators for Modeling and Control of Autonomous Vehicles

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 pure 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. A multi-step prediction loss function is used in the training process, enabling a long-term prediction capability. Furthermore, a data-driven model predictive controller with the learned Koopman model is designed for velocity profile tracking control of autonomous vehicles. Simulation results in a high-fidelity CarSim environment show that our approach outperforms previously developed traditional and advanced modeling methods. Velocity profile tracking tests of the autonomous vehicle are also performed in the CarSim environment. The results show that our approach has better tracking accuracy and higher computational efficiency than the model predictive control algorithms using a nonlinear model and a linear time-varying model.