Willems' fundamental lemma for linear descriptor systems and its use for data-driven output-feedback MPC

TL;DR

This paper extends Willems' fundamental lemma to linear descriptor systems, enabling data-driven predictive control with less data and providing stability conditions for output-feedback model predictive control.

Contribution

It introduces a variant of Willems' lemma tailored for descriptor systems and develops a data-driven control framework with stability guarantees.

Findings

Descriptor systems require less data for non-parametric modeling.

A data-driven predictive control method is proposed for descriptor systems.

Stability conditions for receding-horizon control are established.

Abstract

In this paper we investigate data-driven predictive control of discrete-time linear descriptor systems. Specifically, we give a tailored variant of Willems' fundamental lemma, which shows that for descriptor systems the non-parametric modelling via a Hankel matrix requires less data compared to linear time-invariant systems without algebraic constraints. Moreover, we use this description to propose a data-driven framework for optimal control and predictive control of discrete-time linear descriptor systems. For the latter, we provide a sufficient stability condition for receding-horizon control before we illustrate our findings with an example.