Stability Analysis of Real-Time Methods for Equality Constrained NMPC

TL;DR

This paper proves asymptotic stability for real-time equality constrained NMPC methods, showing that with sufficiently short sampling times, the combined system-optimizer dynamics remain stable, extending existing results.

Contribution

It provides a formal proof of asymptotic stability for a class of real-time NMPC methods with single optimizer iterations per sampling period.

Findings

Asymptotic stability is guaranteed with short sampling times.

Extends stability results for real-time iteration strategies.

Applicable to Q-linearly convergent online optimization methods.

Abstract

In this paper, a proof of asymptotic stability for the combined system-optimizer dynamics associated with a class of real-time methods for equality constrained nonlinear model predictive control is presented. General Q-linearly convergent online optimization methods are considered and asymptotic stability results are derived for the case where a single iteration of the optimizer is carried out per sampling time. In particular, it is shown that, if the underlying sampling time is sufficiently short, asymptotic stability can be guaranteed. The results constitute an extension to existing attractivity results for the well-known real-time iteration strategy.