Nonlinear System Identification with Regularized Local FIR Model Networks

Abstract

An algorithm for the identification of nonlinear black-box systems is introduced using novel techniques for the regularized estimation of impulse responses for linear systems. Based on a comparison of the advantages and disadvantages of (N) FIR and (N) ARX model structures for the linear and nonlinear case it is outlined that the novel regularized FIR model estimation removes the major drawback of high parameter variance from the FIR model and makes it thus usable as a local model structure in local model networks. The estimation of the local FIR models is performed with a special regularization matrix, which is derived from the concept of reproducing kernel Hilbert spaces incorparating the knowledge of the exponential decay of the impulse response of a stable system. The algorithm is applied to a test system and is, in contrast to local ARX models, always able to achieve stability and a fairly good prediction accuracy.