On a Continuous-Time Version of Willems’ Lemma
Victor G. Lopez, Matthias A. Müller
Abstract
In this paper, a method to represent every input-output trajectory of a continuous-time linear system in terms of previously collected data is presented. This corresponds to a continuous-time version of the well-known Willems’ lemma. The result is obtained by sampling the continuous signals at regular intervals, and constructing Hankel-like structures that closely resemble their discrete-time counterparts. Then, it is shown how to use measured persistently excited data to design a time-varying vector of parameters that allows the generation of arbitrary piecewise differentiable trajectories. A class of input signals that satisfies the conditions for persistence of excitation is also provided.
Topics & Concepts
Lemma (botany)PiecewiseTrajectoryDifferentiable functionSampling (signal processing)Discrete time and continuous timeMathematicsPiecewise linear functionClass (philosophy)AlgorithmApplied mathematicsComputer scienceControl theory (sociology)Mathematical analysisControl (management)PhysicsStatisticsFilter (signal processing)EcologyBiologyPoaceaeAstronomyComputer visionArtificial intelligenceControl Systems and IdentificationFault Detection and Control SystemsProbabilistic and Robust Engineering Design