Real-Time Trajectory Tracking at Handling Limits: An Iterative Bandwidth-Regularized Sparse GP-MPC Approach

Trajectory tracking at handling limits poses a critical challenge for autonomous driving systems, where parameter uncertainties and highly nonlinear tire dynamics necessitate adaptive control. However, standard adaptive implementations often exhibit instability. For instance, while Gaussian Process Model Predictive Control (GP-MPC) can theoretically correct model mismatches, standard implementations suffer from overfitting-induced control chattering driven by unconstrained likelihood maximization on noisy data. In this paper, we present a Bandwidth-regularized Sparse GP-MPC scheme to address this issue by combining a Subset of Data (SoD) Sparse GP approximation with a physically-consistent hyperparameter clamping strategy. Specifically, bounding the kernel lengthscale imposes a strict spectral bandwidth limit. This essentially prevents the model from fitting high-frequency noise beyond the physical limits of the actuators. Co-simulation tests confirm that our regularized approach resolves the severe control chattering seen in baseline GP-MPC. The vehicle recovers a smooth transient behavior that closely matches the nominal reference, yielding reduced overshoot, faster settling times, and better overall tracking precision.