论文标题
采样定理，以精确识别连续时间非线性动力学系统
A Sampling Theorem for Exact Identification of Continuous-time Nonlinear Dynamical Systems
论文作者
论文摘要
低采样频率挑战了从采样数据的连续时间（CT）动态系统的确切识别，即使其模型是可识别的。提出了必要且充分的条件 - 是从Koopman运营商构建的 - 从采样数据中确切识别CT系统。该条件给出了具有Koopman不变子空间的CT非线性动力学系统的精确识别的Nyquist-Shannon样的临界频率：1）它为采样频率建立了足够的条件，该采样频率允许样本离散序列以发现基本系统和2）的条件，并为采样频率建立了一个必要的系统。 3）原始CT信号不必按照Nyquist-Shannon定理的频带限制。理论标准已在许多模拟示例上进行了证明，包括线性系统，具有平衡的非线性系统和限制周期。
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.
