Feasibility Governor for Linear Model Predictive Control

TL;DR

This paper presents the Feasibility Governor, an add-on for linear MPC that enlarges the feasible region, guarantees recursive feasibility, and ensures constraint satisfaction and stability through offline and online convex optimization.

Contribution

The Feasibility Governor is a novel add-on that enhances linear MPC by enlarging the feasible region and guaranteeing recursive feasibility with a convex quadratic program.

Findings

Enlarges the region of attraction for linear MPC.

Guarantees recursive feasibility and constraint satisfaction.

Achieves asymptotic stability and zero-offset tracking.

Abstract

This paper introduces the Feasibility Governor (FG): an add-on unit that enlarges the region of attraction of Model Predictive Control by manipulating the reference to ensure that the underlying optimal control problem remains feasible. The FG is developed for linear systems subject to polyhedral state and input constraints. Offline computations using polyhedral projection algorithms are used to construct the feasibility set. Online implementation relies on the solution of a convex quadratic program that guarantees recursive feasibility. The closed-loop system is shown to satisfy constraints, achieve asymptotic stability, and exhibit zero-offset tracking.