Optimality Conditions for Model Predictive Control: Rethinking Predictive Model Design

TL;DR

This paper establishes fundamental conditions on predictive models that determine the optimality of Model Predictive Control (MPC), challenging traditional modeling approaches and providing a new foundation for designing models that improve MPC performance.

Contribution

It introduces necessary and sufficient conditions on prediction models for MPC optimality, offering a novel theoretical framework that links model design directly to control performance.

Findings

Derived conditions for model-based MPC optimality

Challenged traditional data-fitting model design

Provided a mathematical foundation for predictive model construction

Abstract

Optimality is a critical aspect of Model Predictive Control (MPC), especially in economic MPC. However, achieving optimality in MPC presents significant challenges, and may even be impossible, due to inherent inaccuracies in the predictive models. Predictive models often fail to accurately capture the true system dynamics, such as in the presence of stochasticity, leading to suboptimal MPC policies. In this paper, we establish the necessary and sufficient conditions on the underlying prediction model for an MPC scheme to achieve closed-loop optimality. Interestingly, these conditions are counterintuitive to the traditional approach of building predictive models that best fit the data. These conditions present a mathematical foundation for constructing models that are directly linked to the performance of the resulting MPC scheme.