Fundamental Lemma for Data-Driven Analysis of Linear Parameter-Varying Systems
Chris Verhoek, Roland Tóth, Sofie Haesaert, Anne Koch
Abstract
Based on the Fundamental Lemma by Willems et al., the entire behaviour of a Linear Time-Invariant (LTI) system can be characterised by a single data sequence of the system as long the input is persistently exciting. This is an essential result for data-driven analysis and control. In this work, we aim to generalise this LTI result to Linear Parameter-Varying (LPV) systems. Based on the behavioural framework for LPV systems, we prove that one can obtain a result similar to Willems’. Based on an LPV representation, i.e., embedding, of nonlinear systems, this allows the application of the Fundamental Lemma for systems beyond the linear class.
Topics & Concepts
Lemma (botany)Linear systemLTI system theoryEmbeddingRepresentation (politics)Control theory (sociology)Sampled data systemsNonlinear systemMathematicsInvariant (physics)Sequence (biology)Computer scienceControl systemApplied mathematicsControl (management)Mathematical analysisEngineeringArtificial intelligenceQuantum mechanicsPolitical scienceGeneticsLawPoaceaePoliticsBiologyEcologyMathematical physicsElectrical engineeringPhysicsControl Systems and IdentificationAdvanced Control Systems OptimizationFault Detection and Control Systems