Data-enabled predictive control with instrumental variables: the direct equivalence with subspace predictive control

Direct data-driven control has attracted substantial interest since it enables optimization-based control without the need for a parametric model. This paper presents a new Instrumental Variable~(IV) approach to Data-enabled Predictive Control (DeePC) that results in favorable noise mitigation properties, and demonstrates the direct equivalence between DeePC and Subspace Predictive Control (SPC). The methodology relies on the derivation of the characteristic equation in DeePC along the lines of subspace identification algorithms. A particular choice of IVs is presented that is uncorrelated with future noise, but at the same time highly correlated with the data matrix. A simulation study demonstrates the improved performance of the proposed algorithm in the presence of process and measurement noise.