Nonlinear system identification using two-dimensional wavelet-based state-dependent parameter models

Abstract

This article presents a nonlinear system identification approach that uses a two-dimensional (2-D) wavelet-based state-dependent parameter (SDP) model. In this method, differing from our previous approach, the SDP is a function with respect to two different state variables, which is realised by the use of a 2-D wavelet series expansion. Here, an optimised model structure selection is accomplished using a PRESS-based procedure in conjunction with orthogonal decomposition (OD) to avoid any ill-conditioning problems associated with the parameter estimation. Two simulation examples are provided to demonstrate the merits of the proposed approach.

Keywords:

• nonlinear systems
• identification for control
• nonlinear system identification
• PRESS statistics
• multivariable nonlinearities

Notes

Notes

1. The mother wavelet has nonzero values within this range. Outside this range, it has zero or insignificant values which are assumed to be zero.

2. A small value of i _min results in a large number of wavelet elements with higher frequency characteristics to be contained in the function's library. And vice versa, with a large value of i _max, the function's library will consist of a large number of wavelet elements that are at lower frequency features.

3. The difference between the overparameterised (original) model's PRESS value and the one calculated by excluding a term from the original model.

4. That is, the output obtained by generating the deterministic model output from the model input alone, without any reference to the output measurements.