A Sampling Theorem for Exact Identification of Continuous-time Nonlinear Dynamical Systems

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.