Adaptive Deep Koopman Operator for Vehicle Dynamics Modeling: A Physics-Informed and Tire-Force-Driven Approach

Accurate and adaptive modeling of vehicle dynamics is paramount for the safety of autonomous driving systems, particularly under extreme maneuvers and time-varying parameters. While Deep Koopman operator theory offers a promising global linearization framework, its online application faces a theoretical bottleneck: the high-dimensional lifted state space inherently induces a rank-deficient problem, rendering traditional recursive least squares based updates numerically unstable. To address this, we propose a novel tire-force-driven modeling framework with guaranteed online stability. First, an offline Deep Koopman model is constructed by embedding 7DOF dynamic equilibrium constraints into the learning objective, ensuring the structural fidelity and physical interpretability of the lifted manifold. Second, we theoretically reformulate the operator update in the rank-deficient space as a minimum-norm solution problem. A Physics-Informed Variable Step-Size Normalized Least Mean Squares (PI-VSS-NLMS) algorithm is proposed, which leverages the projection property of NLMS to act as a stable pseudo-inverse solver while incorporating an anchoring mechanism to suppress parameter drift. Extensive simulations on CarSim and Hardware-in-the-Loop validation on dSPACE MicroAutobox III confirm the superiority of the proposed algorithm. It achieves robust prediction accuracy under unseen excitations while guaranteeing real-time feasibility with an average execution time of 0.421 ms, thus bridging the gap between theoretical models and practical deployment.