This paper shows a way to predict and control systems whose dynamics change with a measurable signal. The authors work with linear parameter‑varying (LPV) models, where the usual linear equations depend on a scheduling signal that the operator can measure. They derive a data-driven predictor that separates the effects of past measurements, future control inputs, the scheduling trajectory, and random innovations (noise). By projecting that predictor onto the space spanned by recorded input‑output‑scheduling data, they obtain an estimator that is asymptotically unbiased — meaning it becomes accurate as the amount of data grows — and that can be used directly inside a receding‑horizon control problem without first identifying a full LPV model.

To make the approach practical, the authors address two main computational problems that arise in LPV data methods. First, LPV predictors grow quickly in dimension because regressors depend on products of scheduling variables over time. Second, naive data formulations make the online optimization problem grow with the dataset size. The paper introduces an LPV extension of γ‑DDPC (gamma data‑driven predictive control) using an LQ factorization of the data matrices. That reformulation fixes the number of online decision variables so it does not depend on how much offline data was collected.

The authors also propose a reduced‑order predictor to curb the exponential growth of scheduling‑dependent regressors. This two‑stage complexity reduction first prunes high‑order scheduling monomials after normalizing the scheduling signal. Then it uses a relevance‑based row selection to keep only the most informative rows of the past and future data matrices. These steps reduce the online problem size and relax the persistence‑of‑excitation requirement (a technical condition on how richly the system was probed during data collection).