A Sampling Theorem for Exact Identification of Continuous-time Nonlinear Dynamical Systems
Abstract
Low sampling frequency challenges the exact identification of the continuous-time (CT) dynamical system from sampled data, even when its model is identifiable. The necessary and sufficient condition is proposed -- which is built from Koopman operator -- to the exact identification of the CT system from sampled data. The condition gives a Nyquist-Shannon-like critical frequency for exact identification of CT nonlinear dynamical systems with Koopman invariant subspaces: 1) it establishes a sufficient condition for a sampling frequency that permits a discretized sequence of samples to discover the underlying system and 2) it also establishes a necessary condition for a sampling frequency that leads to system aliasing that the underlying system is indistinguishable; and 3) the original CT signal does not have to be band-limited as required in the Nyquist-Shannon Theorem. The theoretical criterion has been demonstrated on a number of simulated examples, including linear systems, nonlinear systems with equilibria, and limit cycles.
Cite
@article{arxiv.2204.14021,
title = {A Sampling Theorem for Exact Identification of Continuous-time Nonlinear Dynamical Systems},
author = {Zhexuan Zeng and Zuogong Yue and Alexandre Mauroy and Jorge Goncalves and Ye Yuan},
journal= {arXiv preprint arXiv:2204.14021},
year = {2022}
}