Model predictive control for tracking using artificial references: Fundamentals, recent results and practical implementation

TL;DR

This paper offers a comprehensive tutorial on MPC for tracking with artificial references, highlighting its benefits, theoretical guarantees, recent advances, and practical implementation aspects.

Contribution

It introduces the concept of artificial references in MPC, reviews recent developments, and discusses implementation and learning-based extensions.

Findings

Guaranteed recursive feasibility under reference changes

Asymptotic stability and increased domain of attraction

Extensions to nonlinear and learning-based MPC

Abstract

This paper provides a comprehensive tutorial on a family of Model Predictive Control (MPC) formulations, known as MPC for tracking, which are characterized by including an artificial reference as part of the decision variables in the optimization problem. These formulations have several benefits with respect to the classical MPC formulations, including guaranteed recursive feasibility under online reference changes, as well as asymptotic stability and an increased domain of attraction. This tutorial paper introduces the concept of using an artificial reference in MPC, presenting the benefits and theoretical guarantees obtained by its use. We then provide a survey of the main advances and extensions of the original linear MPC for tracking, including its non-linear extension. Additionally, we discuss its application to learning-based MPC, and discuss optimization aspects related to its implementation.