Multiobjective Nonlinear Identification

Abstract

The identification of nonlinear systems can be posed as a nonlinear functional approximation problem. From the Weierstrass Theorem (Powell, 1981) and the Kolmogorov theorem (Sprecher, 1965) in approximation theory, it is shown that the polynomial and many other approximation schemes can approximate a continuous function arbitrarily well. In recent years, a number of nonlinear system identification approaches, particularly identification using neural networks, based on the universal approximation theorem (Cybenko, 1989), are applications of a similar mathematical approach.