A Generalized Stopping Criterion for Real-Time MPC with Guaranteed Stability
Abstract
Most of the real-time implementations of the stabilizing optimal control actions suffer from the necessity to provide high computational effort. This paper presents a cutting-edge approach for real-time evaluation of linear-quadratic model predictive control (MPC) that employs a novel generalized stopping criterion, achieving asymptotic stability in the presence of input constraints. The proposed method evaluates a fixed number of iterations independent of the initial condition, eliminating the necessity for computationally expensive methods. We demonstrate the effectiveness of the introduced technique by its implementation of two widely-used first-order optimization methods: the projected gradient descent method (PGDM) and the alternating directions method of multipliers (ADMM). The numerical simulation confirmed a significantly reduced number of iterations, resulting in suboptimality rates of less than 2\,\%, while the effort reductions exceeded 80\,\%. These results nominate the proposed criterion for an efficient real-time implementation method of MPC controllers.
Cite
@article{arxiv.2309.04444,
title = {A Generalized Stopping Criterion for Real-Time MPC with Guaranteed Stability},
author = {Kristína Fedorová and Yuning Jiang and Juraj Oravec and Colin N. Jones and Michal Kvasnica},
journal= {arXiv preprint arXiv:2309.04444},
year = {2023}
}