Identification of nonlinear systems with a state-dependent ARX model

Abstract

The utility of linear stochastic models is well known. By developing a straight forward, time-domain method of determining nonlinear coefficients for stochastic models, this paper expands the utility for nonlinear systems. A single-input multiple-output nonlinear identification algorithm is formulated and demonstrated for systems that exhibit both soft and hard nonlinearities. The identification method is based on an Auto Regressive Exogenous stochastic model. The nonlinear characteristics of the system being identified are represented with coefficients that are a function of the output states. These coefficients are formulated using linear combinations of orthogonal vectors chosen from basis sets. The effects of noise on the input and outputs are minimized by utilizing a Generalized Least Squares algorithm. The developed identification method is demonstrated on a nonlinear numerical example with simulated corrupted measurements. ©2010 Society for Experimental Mechanics Inc.