Physics-Informed Adaptive Deep Koopman Operator Modeling for Autonomous Vehicle Dynamics

Koopman operator has been recognized as an ongoing data-driven modeling method for vehicle dynamics which lifts the original state space into a high-dimensional linear state space. The deep neural networks (DNNs) are verified to be useful for the approximation of Koopman operator. To further improve the accuracy of Koopman operator approximation, this paper introduces a physical loss function term from the concept of physics-informed neural networks (PINNs), i.e., the acceleration loss between neural network output and sensor measurements, to improve the efficiency of network learning and its interpretability. Moreover, we utilize the sliding window least squares (SWLS) to update the system matrix and input matrix online in the lifted space, therefore enabling the deep Koopman operator to adapt to the rapid dynamics of autonomous vehicles in real events. The data collection and validation are conducted on CarSim/Simlink co-simulation platform. With comparison to other physics-based and data-driven approaches on various scenarios, the results reveal that the acceleration loss-informed network refines the accuracy of Koopman operator approximation and renders it with inherent generalization, and the SWLS enforces the deep Koopman operator's capability to cope with changes in vehicle parameters, road conditions, and rapid maneuvers. This indicates the proposed physics-informed adaptive deep Koopman operator is a performant and efficient data-driven modeling tool.