A Feasibility Governor for Enlarging the Region of Attraction of Linear Model Predictive Controllers

TL;DR

This paper introduces a Feasibility Governor (FG) that enlarges the region of attraction for linear MPCs by manipulating reference commands, ensuring feasibility, stability, and improved tracking in constrained control systems.

Contribution

The paper presents a novel add-on unit, the FG, which uses offline polyhedral projections and online quadratic programming to enhance the robustness and feasibility of linear MPCs.

Findings

Ensures constraint satisfaction and asymptotic stability.

Enlarges the region of attraction for linear MPC.

Achieves finite-time convergence of the reference.

Abstract

This paper proposes a method for enlarging the region of attraction of Linear Model Predictive Controllers (MPC) when tracking piecewise-constant references in the presence of pointwise-in-time constraints. It consists of an add-on unit, the Feasibility Governor (FG), that manipulates the reference command so as to ensure that the optimal control problem that underlies the MPC feedback law remains feasible. Offline polyhedral projection algorithms based on multi-objective linear programming are employed to compute the set of feasible states and reference commands. Online, the action of the FG is computed by solving a convex quadratic program. The closed-loop system is shown to satisfy constraints, be asymptotically stable, exhibit zero-offset tracking, and display finite-time convergence of the reference.