Physics-Informed Imitation Learning for Resilient Autonomous Driving
Imitation learning has emerged as a promising paradigm for autonomous vehicle control. However, existing policies often suffer from severe covariate shift and lack explicit stability guarantees in closed-loop trajectory tracking. This paper proposes an adaptive Lyapunov-constrained imitation learning framework for vehicle trajectory tracking. To address the covariate shift problem, we explicitly embed a discrete-time kinematic bicycle model into the policy training process. This differentiable physical prior enables propagation of the nominal tracking error and allows a global Lyapunov decay constraint to be directly employed on the policy optimization via an Actor-Critic architecture. To prevent the overly aggressive penalization near the reference trajectory, we introduce a state-dependent adaptive decay rate that relaxes the constraint for small errors while strengthening it under large deviations. As a result, the proposed method achieves both high tracking precision and strong recovery from model uncertainties and disturbances. Extensive experiments in interactive traffic environments demonstrate that the proposed method significantly outperforms state-of-the-art baselines in collision avoidance and disturbance rejection.