On the relationship between data-enabled predictive control and subspace predictive control

TL;DR

This paper explores the theoretical relationship between data-enabled predictive control (DeePC) and subspace predictive control (SPC), demonstrating their equivalence in deterministic cases and analyzing their differences under noise conditions.

Contribution

It establishes the equivalence of DeePC and SPC in deterministic settings and examines their comparative advantages and limitations with noisy data.

Findings

DeePC and SPC are equivalent in deterministic systems.

Both methods show differences in handling measurement noise.

Simulation illustrates the practical implications of their differences.

Abstract

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.