  Data-enabled predictive control (DeePC) is a recently proposed approach that
combines system identification, estimation and control in a single optimization
problem, for which only recorded input/output data of the examined system is
required. The same premise holds for the subspace predictive control (SPC)
method in which a multi-step prediction model is identified from the same data
as required for DeePC. This model is then used to formulate a similar optimal
control problem. In this work we investigate the relationship between DeePC and
SPC. Our primary contribution is to show that SPC is equivalent to DeePC in the
deterministic case. We also show the equivalence of both methods in a special
case for the non-deterministic formulation. We investigate the advantages and
shortcomings of DeePC as opposed to SPC with and without measurement noise and
illustrate them with a simulation example.
