Wiener-NN models and robust identification

The robust identification principles of linear systems on the basis of n-width measure can be applied in dynamic nonlinear systems by using Wiener neural net (NN) structure. The reduced Wiener model consists of a cascade of Laguerre dynamics and static polynomial mapping. In Wiener-NN model the static nonlinear mapping is realized with NN. The space spanned by the continuous Laguerre functions is an optimal n-dimensional subspace in the n-width sense for a set of transfer functions having poles inside a certain disk by Wahlberg and Makila (1995). When a damped or slightly oscillating nonlinear system is linearized in all possible operating points, the corresponding poles define a certain closed set. If the disk referred above is parameterized so that it covers this set of poles, the corresponding Laguerre functions is an (heuristically) optimal n-dimensional subspace in the n-width sense for this nonlinear system in the Wiener context. Kautz functions form an (heuristically) optimal basis for a nonlinear dynamic system having dominating resonant mode. Chromatographic separation case is shortly demonstrated.