Study on the modeling of nonlinear time variant systems based on neural networks combined with basis sequence expansions

This paper presents a new method for identifying nonlinear time variant systems. The method asks for the implementation of a procedure developed for time-variant linear systems using wavelets by Tsatsanis and Giannakis. An extension to nonlinear models is considered. The essential idea is that we regard the weights of the feedforward neural networks as a time-variant parametric vector that reflects the time-variant dynamics of the system and then this time-variant parametric vector can be expanded onto a finite set of basis sequences. Thus, a parsimonious model can be realized by this method. In order to improve the real-time capability of the algorithm, the network is trained by a simple fast learning algorithm based on the local least squares presented by the authors. The method is tested by numerical experiment.