Stability-Aware Imitation Learning from Model Predictive Control for Autonomous Vehicle Lateral Control: Exact Q-Loss and a Novel Training Procedure

Abstract

This paper develops a certified imitation-learning framework for approximating model predictive control (MPC) policies with feedforward neural controllers and validates it on autonomous-vehicle lateral control. An exact finite-horizon Q-loss is constructed by fixing the learner's first steering action in the expert MPC problem and re-optimizing the remaining horizon, thereby measuring its downstream optimal-control consequence rather than only pointwise action mismatch. The neural policy is represented as a linear fractional transformation (LFT) interconnection with activation nonlinearities described by sector integral quadratic constraints (IQCs). Combined with a quadratic Lyapunov condition, this representation yields a differentiable certification margin based on the largest eigenvalue of the Lyapunov-IQC matrix. The margin is enforced during training through a logarithmic barrier, while certified Dataset Aggregation (DAgger) and safe projection keep data-aggregation rollouts within the certified policy set. Experiments on a CAD-referenced autonomous-vehicle platform with AprilTag localization and real-time steering demonstrate the resulting closed-loop performance.