  Data-driven control uses a past signal trajectory to characterise the
input-output behaviour of a system. Willems' lemma provides a data-based
prediction model allowing a control designer to bypass the step of identifying
a state-space or transfer function model. This paper provides a more
parsimonious formulation of Willems' lemma that separates the model into
initial condition matching and predictive control design parts. This avoids the
need for regularisers in the predictive control problem that are found in other
data-driven predictive control methods. It also gives a closed form expression
for the optimal (minimum variance) unbiased predictor of the future output
trajectory and applies it for predictive control. Simulation comparisons
illustrate very good control performance.
