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A prediction-error estimation algorithm is developed for nonlinear discrete-time systems which can be represented by the output-affine difference equation model. The theory of hypothesis testing is employed to select a model with the correct structure. Problems relating to the use of output-affine models in the identification of nonlinear systems are discussed and a comparison with the NARMAX (Nonlinea ARMAX) model is given.
Chen et al. (1988) studied this question.