Robust contraction-based model predictive control for nonlinear systems

TL;DR

This paper introduces a robust contraction-based model predictive control method for nonlinear perturbed systems that simplifies design by avoiding terminal constraints and guarantees stability with minimal prediction horizon.

Contribution

It proposes a novel MPC approach leveraging system properties to ensure stability without terminal constraints, suitable for nonlinear systems with model mismatches.

Findings

Guarantees closed-loop stability under perturbations

Eliminates the need for terminal constraints in MPC

Uses shortest prediction horizon for stability

Abstract

Model Predictive Control (MPC) is a widely known control method that has proved to be particularly effective in multivariable and constrained control. Closed-loop stability and recursive feasibility can be guaranteed by employing accurate models in prediction and suitable terminal ingredients, i.e. the terminal cost function and the terminal constraint. Issues might arise in case of model mismatches or perturbed systems, as the state predictions could be inaccurate, and nonlinear systems for which the computation of the terminal ingredients can result challenging. In this manuscript, we exploit the properties of component-wise uniformly continuous and stabilizable systems to introduce a robust contraction-based MPC for the regulation of nonlinear perturbed systems, that employs an easy-to-design terminal cost function, does not make use of terminal constraints, and selects the shortest prediction horizon that guarantees the stability of the closed-loop system.