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

TL;DR

This paper introduces a local sensitivity analysis method for ARX-based data-driven predictive control, enabling better uncertainty quantification and regularization shaping, especially in weak-excitation scenarios.

Contribution

It derives a first-order linearization of the implicit multi-step predictor, providing a new sensitivity metric and uncertainty estimate for improved control robustness.

Findings

Sensitivity analysis is most effective in weak-excitation regimes.

The proposed method offers additional robustness gains over baseline regularization.

Numerical results validate the usefulness of the sensitivity analysis.

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.