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

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.

Data-Driven Robust Control for Discrete Linear Time-Invariant Systems: A Descriptor System Approach

“…Besides, researchers in [3] introduced the concept of data-informativity, which answered the question that what sufficient conditions should those data sets possess for systems' analysis and control. Subsequent works have extended DDC methods in the behavioral theory to various scenarios, such as multiple data sets [4], data-based controllability [5] and observability [6] tests, linear time-varying systems [7], switched linear systems [8], descriptor systems [9], nonlinear systems [10] and linear delay systems [11]. Moreover, data-driven model predictive control was considered in [12] and [13].…”