Willems’ Fundamental Lemma for Linear Descriptor Systems and Its Use for Data-Driven Output-Feedback MPC
Philipp Schmitz, Timm Faulwasser, Karl Worthmann
Abstract
In this letter 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 modeling 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.
Topics & Concepts
Model predictive controlControl theory (sociology)Lemma (botany)Algebraic numberLTI system theoryLinear systemParametric statisticsDiscrete time and continuous timeStability (learning theory)Computer scienceInvariant (physics)Matrix (chemical analysis)MathematicsControl (management)Artificial intelligenceMachine learningStatisticsBiologyMaterials sciencePoaceaeMathematical analysisMathematical physicsEcologyComposite materialAdvanced Control Systems OptimizationControl Systems and IdentificationFault Detection and Control Systems