Nonlinear Systems Modeling Using Polynomial Neural Networks: Comparison

Abstract

Nonlinear systems have not been extensively utilized in engineering research. This is a consequence of the lack of effective analytical approaches analogous to those developed for linear systems, which are well understood and readily analyzable. This paper presents the application of two artificial neural networks (ANNs) for online identification of nonlinear systems as an alternative to linear systems theory. To illustrate this, the nonlinear model of a single inverted pendulum on a cart (SIPC) was identified from experimental data obtained from a laboratory prototype. The model structure employed in this study was based on the nonlinear autoregressive model with exogenous inputs (NARX) on Volterra polynomial basis function (VPBF) and Chebyshev polynomial basis function (CPBF) neural networks. The neural network structures were trained with experimental data from the SIPC prototype, which was recorded for a duration of 60 seconds. Subsequently, these models were validated using experimental data from a separate 15-second recording. The neural networks with Chebyshev polynomials demonstrated slightly superior performance.