  Based on the extension of the behavioral theory and the Fundamental Lemma for
Linear Parameter-Varying (LPV) systems, this paper introduces a Data-driven
Predictive Control (DPC) scheme capable to ensure reference tracking and
satisfaction of Input-Output (I/O) constraints for an unknown system under the
conditions that (i) the system can be represented in an LPV form and (ii) an
informative data-set containing measured I/O and scheduling trajectories of the
system is available. It is shown that if the data set satisfies a persistence
of excitation condition, then a data-driven LPV predictor of future
trajectories of the system can be constructed from the I/O data set and online
measured data. The approach represents the first step towards a DPC solution
for nonlinear and time-varying systems due to the potential of the LPV
framework to represent them. Two illustrative examples, including reference
tracking control of a nonlinear system, are provided to demonstrate that the
LPV-DPC scheme, purely based on data, achieves similar performance as LPV
model-based predictive control.
