We study local sensitivity of structured ARX-based data-driven predictive control. Although predictor estimation is linear in the ARX parameters, the lifted multi-step predictor used in MPC depends on them implicitly, which complicates both uncertainty propagation and task-aware regularization. We derive a local first-order linearization of this implicit predictor map. The resulting Jacobian yields both an approximate control-relevant prediction uncertainty term and a task-dependent sensitivity metric for shaping kernel regularization. Numerical results show that the proposed analysis is most useful in weak-excitation regimes, where baseline SS regularization already provides substantial robustness gains and the proposed sensitivity shaping yields a further smaller improvement.
@article{arxiv.2604.05832,
title = {Local Sensitivity Analysis for Kernel-Regularized ARX Predictors in Data-Driven Predictive Control},
author = {Aihui Liu and Magnus Jansson},
journal= {arXiv preprint arXiv:2604.05832},
year = {2026}
}