  Data-driven predictive control (DPC) is becoming an attractive alternative to
model predictive control as it requires less system knowledge for
implementation and reliable data is increasingly available in smart engineering
systems. Two main approaches exist within DPC, which mostly differ in the
construction of the predictor: estimated prediction matrices (unbiased for
large data) or Hankel data matrices as predictor (allows for optimizing the
bias/variance trade-off). In this paper we develop a novel, generalized DPC
(GDPC) algorithm that constructs the predicted input sequence as the sum of a
known input sequence and an optimized input sequence. The predicted output
corresponding to the known input sequence is computed using an unbiased, least
squares predictor, while the optimized predicted output is computed using a
Hankel matrix based predictor. By combining these two types of predictors, GDPC
can achieve high performance for noisy data even when using a small Hankel
matrix, which is computationally more efficient. Simulation results for a
benchmark example from the literature show that GDPC with a minimal size Hankel
matrix can match the performance of data-enabled predictive control with a
larger Hankel matrix in the presence of noisy data.
