Offset-free model predictive control: stability under plant-model mismatch

TL;DR

This paper introduces a nonlinear offset-free MPC method that guarantees stability and offset-free performance despite plant-model mismatch and disturbances, addressing a longstanding challenge in the field.

Contribution

It provides the first general stability analysis for nonlinear offset-free MPC, incorporating robustness to plant-model mismatch and disturbances.

Findings

Proves nominal stability and offset-free performance.

Demonstrates robustness to estimation errors and disturbances.

Extends results to small plant-model mismatches.

Abstract

We present the first general stability results for nonlinear offset-free model predictive control (MPC). Despite over twenty years of active research, the offset-free MPC literature has not shaken the assumption of closed-loop stability for establishing offset-free performance. In this paper, we present a nonlinear offset-free MPC design that is robustly stable with respect to the tracking errors, and thus achieves offset-free performance, despite plant-model mismatch and persistent disturbances. Key features and assumptions of this design include quadratic costs, differentiability of the plant and model functions, constraint backoffs at steady state, and a robustly stable state and disturbance estimator. We first establish nominal stability and offset-free performance. Then, robustness to state and disturbance estimate errors and setpoint and disturbance changes is demonstrated. Finally, the results are extended to sufficiently small plant-model mismatch. The results are illustrated by numerical examples.