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The paper describes a system identification method for a nonlinear system based on a multi-point linear approximation. We show that under mild assumptions, the task can be transformed into a series of one-dimensional approximations, for which we propose an efficient solution method based on solving simple nonlinear programs (NLPs). The approach provides identification of nonlinear systems in a polynomial model structure (ARX,OE,BJ) from input-output data. The approximation is based on a neural network modelling procedure. The proposed modelling procedure is characterized by fast training, adjustable accuracy and reduced complexity of the final model. The modelling technique is widely applicable in automotive, power electronics, computer graphics, etc..

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Given a set of input-output measurements, the paper proposes a method for approximation of a nonlinear system by a piecewise affine model (PWA). First step of the two-stage procedure is identification from input-output data, in order to obtain an appropriate nonlinear function in analytic form. The analytic expression of the model can be represented either by a static nonlinear function or by a dynamic system and can be obtained using a basis function expansion modeling approach. Subsequently we employ nonlinear programming to derive optimal PWA approximation of the identified model such that the approximation error is minimized. Moreover, we show that approximation of multivariate systems can be transformed into a series of one-dimensional approximations, which can be solved efficiently using standard optimization techniques.