Data-Driven Predictive Control and MPC: Do we achieve optimality?

TL;DR

This paper investigates the conditions under which Predictive Control and Data-Driven Predictive Control can achieve closed-loop optimality, highlighting limitations of data-driven approaches and the importance of decision-making structure.

Contribution

It provides sufficient conditions for optimality in Predictive Control and clarifies that data-driven methods' optimality depends on their decision-making formulation rather than data accuracy.

Findings

Conditions for closed-loop optimality in Predictive Control

Data-driven approaches' optimality depends on decision process structure

Improving prediction accuracy alone does not ensure optimal control

Abstract

In this paper, we explore the interplay between Predictive Control and closed-loop optimality, spanning from Model Predictive Control to Data-Driven Predictive Control. Predictive Control in general relies on some form of prediction scheme on the real system trajectories. However, these predictions may not accurately capture the real system dynamics, for e.g., due to stochasticity, resulting in sub-optimal control policies. This lack of optimality is a critical issue in case of problems with economic objectives. We address this by providing sufficient conditions on the underlying prediction scheme such that a Predictive Controller can achieve closed-loop optimality. However, these conditions do not readily extend to Data-Driven Predictive Control. In this context of closed-loop optimality, we conclude that the factor distinguishing the approaches within Data-Driven Predictive Control is if they can be cast as a sequential decision-making process or not, rather than the dichotomy of model-based vs. model-free. Furthermore, we show that the conventional approach of improving the prediction accuracy from data may not guarantee optimality.