Lyapunov-Constrained Behavior Cloning for Robust Trajectory Tracking in Autonomous Driving

Imitation Learning methods (such as behavior cloning) have achieved significant success in the field of autonomous driving, but they are inherently limited by poor stability, error accumulation, and a lack of formal guarantees for strategy robustness and convergence. To address these challenges, we propose Lyapunov-BC, a unified framework that enhances traditional behavior cloning by introducing state space Lyapunov stability constraints with parameter space regulariza-tion, ensuring robust trajectory dynamics and smooth policy updates. Theoretically, we prove that Lyapunov-BC achieves exponential decay of tracking error and converges to a stable policy solution. Extensive experiments in simulated intersection scenarios demonstrate that Lyapunov-BC significantly outper-forms some imitation learning algorithms in terms of trajectory tracking accuracy, control signal smoothness, and robustness against adversarial or out-of-distribution neighbor behavior. Furthermore, our analysis indicates that Lyapunov-BC maintains reliable performance even under severe distribution shifts where baseline imitation learning methods fail. These results highlight the effectiveness and practicality of Lyapunov-regularized imitation learning in achieving robust and safe trajectory tracking.