Kernel Identification of Non-Linear Systems with General Structure

Abstract

In the paper we deal with the problem of non-linear dynamic system identification in the presence of random noise. The class of considered systems is relatively general, in the sense that it is not limited to block-oriented structures such as Hammerstein or Wiener models. It is shown that the proposed algorithm can be generalized for two-stage strategy. In step 1 (non-parametric) the system is approximated by multi-dimensional regression functions for a given set of excitations, treated as representative set of points in multi-dimensional space. ‘Curse of dimensionality problem’ is solved by using specific (quantized or periodic) input sequences. Next, in step 2, non-parametric estimates can be plugged into least squares criterion and support model selection and estimation of system parameters. The proposed strategy allows decomposition of the identification problem, which can be of crucial meaning from the numerical point of view. The “estimation points” in step 1 are selected to ensure good task conditioning in step 2. Moreover, non-parametric procedure plays the role of data compression. We discuss the problem of selection of the scale of non-parametric model, and analyze asymptotic properties of the method. Also, the results of simple simulation are presented, to illustrate functioning of the method. Finally, the proposed method is successfully applied in Differential Scanning Calorimeter (DSC) to analyze aging processes in chalcogenide glasses.