Local Sensitivity Analysis for Kernel-Regularized ARX Predictors in Data-Driven Predictive Control
This is an incremental improvement for data-driven predictive control systems, specifically addressing sensitivity analysis in weak-excitation scenarios.
The paper tackles the problem of uncertainty propagation and task-aware regularization in data-driven predictive control with ARX-based predictors by deriving a local first-order linearization of the implicit predictor map. Numerical results show the analysis is most useful in weak-excitation regimes, where it yields a further smaller improvement over baseline regularization.
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.