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Two steps piecewise affine identification of nonlinear systems

Stevek J., Szucs A., Kvasnica M., Fikar M., Kozak S.

Archives of Control Sciences

2012

Vol. 22, no. 4

371-388

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.

An iterative identification based on the Youla-Kucera parameterisation without model reduction

Kozka S., Mikles J., Fikar M.

Archives of Control Sciences

2003

Vol. 13, no. 1

19-31

The aim of this paper is to present an iterative identification of the plant in the presence of feedback using input-output data, based on the Youla-Kucera parameterisation. When a reduced complexity model is identified then the controller is designed. here the identified model is just a vehicle for the computation of a controller. The proposed iterative algorithm contains suitably selected filters and ensures that the model reduction of the identified model is not necessary as in the standard approach. This iterative approach simplifies the identification task of the Youla-Kucera parameter as only its numerator has to be estimated. an experiment with a continuous stirred tank reactor (CSTR), with represents a non-linear single input -single output (SISO)system, illustrate this feature. LQ controller design is used for stabilisation.