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.
Wei et al. (2026) studied this question.