TY - GEN
T1 - A Sampling Theorem for Exact Identification of Continuous-time Nonlinear Dynamical Systems
AU - Zeng, Zhexuan
AU - Yue, Zuogong
AU - Mauroy, Alexandre
AU - Goncalves, Jorge
AU - Yuan, Ye
N1 - Publisher Copyright:
© 2022 IEEE.
PY - 2022
Y1 - 2022
N2 - Low sampling frequency challenges the exact identification of continuous-time (CT) dynamical systems from sampled data, even when its model is identifiable. A necessary and sufficient condition is proposed- which is built from Koopman operator- to the exact identification of the CT system from sampled data. This condition gives a Nyquist-Shannon-like critical frequency for exact identification of CT nonlinear dynamical systems with a set of valid Koopman eigenfunctions: 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. The theoretical criterion has been demonstrated on a number of simulated examples, including linear systems, nonlinear systems with equilibria, and limit cycles.
AB - Low sampling frequency challenges the exact identification of continuous-time (CT) dynamical systems from sampled data, even when its model is identifiable. A necessary and sufficient condition is proposed- which is built from Koopman operator- to the exact identification of the CT system from sampled data. This condition gives a Nyquist-Shannon-like critical frequency for exact identification of CT nonlinear dynamical systems with a set of valid Koopman eigenfunctions: 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. The theoretical criterion has been demonstrated on a number of simulated examples, including linear systems, nonlinear systems with equilibria, and limit cycles.
UR - http://www.scopus.com/inward/record.url?scp=85146994074&partnerID=8YFLogxK
U2 - 10.1109/CDC51059.2022.9992482
DO - 10.1109/CDC51059.2022.9992482
M3 - Conference contribution
AN - SCOPUS:85146994074
T3 - Proceedings of the IEEE Conference on Decision and Control
SP - 6686
EP - 6692
BT - 2022 IEEE 61st Conference on Decision and Control, CDC 2022
PB - Institute of Electrical and Electronics Engineers Inc.
T2 - 61st IEEE Conference on Decision and Control, CDC 2022
Y2 - 6 December 2022 through 9 December 2022
ER -