A PMGOP method of parameter identification for a class of continuous nonlinear systems

Abstract

A series of piecewise multiple general orthogonal polynomials (PMGOPs) is introduced and applied to the parameter identication problem for a class of continuous nonlinear systems. After introducing PMGOPs and discussing their main properties, an effective procedure for the parameter identification of a large class of continuous systems, called parameter separable systems, is proposed. Some relevant algorithms are presented. The procedure given in the paper has the following advantages compared with other methods: the identification algorithm (IA) obtained is computationally fast and accurate; the IA can be implemented in a recursive fashion; the IA is effective for a small number of data points; the IA does not require a priori knowledge of the estimated parameters; the IA is tolerant to choices of expanding orders when PMGOPs are applied. Some numerical examples, together with an experimental example taken from a biochemical fermentation process, are given for illustrative purposes.