A “fundamental lemma” for continuous-time systems, with applications to data-driven simulation. (English) Zbl 1520.93209
Summary: 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
[P. Rapisarda et al., “A persistency of excitation condition for continuous-time systems”, IEEE Control Syst. Lett. 7, 589–594 (2023; doi:10.1109/LCSYS.2022.3205550)], 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.
Keywords:
persistency of excitation; continuous-time linear time-invariant systems; Chebyshev polynomials; data-driven simulationSoftware:
ChebfunReferences:
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