Learning-based MPC for Trajectory Tracking: A Context-Aware Physics-Embedded Mixture-of-Experts for Tire Stiffness Identification

In autonomous vehicle trajectory tracking, model predictive control (MPC) requires accurate knowledge of tire cornering stiffness to maintain precise prediction. Under high speed or low-friction conditions, stiffness varies sharply with road adhesion and cannot be measured directly; once the tire saturates, stiffness estimation becomes ill-conditioned and MPC prediction degrades, ultimately compromising tracking performance. This paper proposes a learning-based MPC framework integrating a Context-Aware Physics-Embedded Mixture-of-Experts (CA-PE MoE) network with recursive least squares (RLS) for online tire stiffness identification. The proposed framework compresses the preceding history of vehicle excitation and lateral response into a low-dimensional operating-context representation and combines it with recent vehicle dynamics to predict tire forces across linear, transition, and saturation regimes through continuous expert blending. RLS extracts cornering stiffness from these predictions and is updated only in the well-conditioned linear region, as indicated jointly by a physics-motivated slip-angle bound and the gating confidence. The identified stiffness updates the MPC prediction model in real time. In variable-friction severe lane change tests using the ISO 3888-2:2011 geometry, the method reduces the closed-loop lateral tracking MAE by 13.6%, 18.4%, and 22.5% at 60, 80, and 100 km/h relative to Static MPC. Additional real-vehicle experiments are conducted to validate the real-world deployment feasibility of the proposed method.