Comparison of Polynomial and Rational Narmax Models for Nonlinear SystemIdentification

摘要

Polynomial and rational expansions of nonlinear stochastic dynamic models arecompared. The structure, approximation properties, identifiability properties, and stability of the NARMAX models are discussed and a unified least squared identification algorithms is introduced. Mathematical models for functional approximation and data approximation are considered. Chaotic behavior, bifurcations, and fractals are addressed. The comparison showed that although the rational model often exhibits superior approximation properties, it is much more difficult to identify compared with the polynomial model.