A Generalized Stopping Criterion for Real-Time MPC with Guaranteed Stability

TL;DR

This paper introduces a novel generalized stopping criterion for real-time linear-quadratic MPC that guarantees stability with reduced computational effort, enabling faster and more efficient control in constrained systems.

Contribution

It proposes a new stopping criterion that evaluates a fixed number of iterations, ensuring stability without extensive computation, applicable to PGDM and ADMM methods.

Findings

Reduced iterations by over 80%

Suboptimality rates below 2%

Guaranteed asymptotic 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.