A deterministic view on explicit data-driven (M)PC

TL;DR

This paper demonstrates that explicit data-driven predictive control (DPC) for linear deterministic systems is as computationally tractable as classical MPC, by analyzing and comparing their optimal control problems and solutions.

Contribution

It establishes the equivalence in complexity between explicit DPC and MPC, clarifying the tractability of data-driven control methods for deterministic systems.

Findings

Explicit solutions to DPC and MPC have the same complexity.

Comparison clarifies the relation between DPC and classical MPC.

Numerical examples illustrate the approach's features.

Abstract

We show that the explicit realization of data-driven predictive control (DPC) for linear deterministic systems is more tractable than previously thought. To this end, we compare the optimal control problems (OCP) corresponding to deterministic DPC and classical model predictive control (MPC), specify its close relation, and systematically eliminate ambiguity inherent in DPC. As a central result, we find that the explicit solutions to these types of DPC and MPC are of exactly the same complexity. We illustrate our results with two numerical examples highlighting features of our approach.