Local Sensitivity Analysis for Kernel-Regularized ARX Predictors in Data-Driven Predictive Control

Aihui Liu; Magnus Jansson

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arXiv · 2604.05832

Local Sensitivity Analysis for Kernel-Regularized ARX Predictors in Data-Driven Predictive Control

Aihui Liu·Magnus Jansson

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Abstract

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.

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Aihui Liu, Magnus Jansson. 2026-04-07. Local Sensitivity Analysis for Kernel-Regularized ARX Predictors in Data-Driven Predictive Control. https://arxiv.org/abs/2604.05832

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