Volterra based nonlinear system identification using fixed pole approach

Identification of nonlinear dynamic systems has received increasing attention since a wide class of physical systems in practice is nonlinear. Identification problem can be defined as the determination of a nonlinear model in a given model class. However, many model structures for nonlinear system identification require a large number of parameters. The overparametrization problem is addressed in this dissertation using an approach via fixed pole basis function expansion. This approach is called Fixed Pole Expansion Technique (FPET) that arises naturally within the Volterra model class. The Volterra model structure provides a relatively simple and general representation for nonlinear system identification where kernel parameters describe the input-output relationship of the nonlinear dynamics. In many cases, the FPET can significantly reduce the number of parameters in a Volterra representation of a nonlinear system. We show that proper selection of fixed pole locations within an FPET structure enables the FPET to achieve considerable advantage over the original Volterra method in terms of both implementation and estimation complexity. In order to select pole locations, we suggest an adaptive algorithm based on gradient descent methodology, and we also develop methods using a priori knowledge of the system class, in which the identified system lies.; The technique of Volterra based FPET is then applied to identification of a satellite transmission channel and to the renal autoregulatory mechanism. We discuss methods to select appropriate pole locations in these applications. The results show that the FPET achieves smaller identification errors, given an equal number of identified parameters, in comparison with truncated Volterra model with finite memory. We also show a reduction in parameter complexity with comparable performance measure.