A “fundamental lemma” for continuous-time systems, with applications to data-driven simulation
Paolo Rapisarda, M. Kanat Camlibel, Henk J. van Waarde
Abstract
We are given one input–output (i-o) trajectory (u,y) produced by a linear, continuous time-invariant system, and we compute its Chebyshev polynomial series representation. We show that if the input trajectory u is sufficiently persistently exciting according to the definition in Rapisarda et al. (2023), then the Chebyshev polynomial series representation of every i-o trajectory can be computed from that of (u,y). We apply this result to data-driven simulation of continuous-time systems.
Topics & Concepts
TrajectoryRepresentation (politics)Lemma (botany)Chebyshev filterChebyshev polynomialsLTI system theoryMathematicsPolynomialSeries (stratigraphy)Time complexityApplied mathematicsLinear systemAlgorithmMathematical analysisPhysicsLawBiologyPoaceaeAstronomyEcologyPaleontologyPolitical sciencePoliticsControl Systems and IdentificationAdvanced Control Systems OptimizationReal-time simulation and control systems