Hammerstein model identification method based on genetic programming

We address a novel approach to identify a nonlinear dynamic system for a Hammerstein model. The Hammerstein model is composed of a nonlinear static block in series with a linear, dynamic system block. The aim of system identification is to provide the optimal mathematical model of both nonlinear static and linear dynamic system blocks in some appropriate sense. We use genetic programming to determine the functional structure for the nonlinear static block. Each individual in genetic programming represents a nonlinear function structure. The unknown parameters of the linear dynamic block and the nonlinear static block given by each individual are estimated with a least square method. The fitness is evaluated by AIC (Akaike information criterion) as representing the balance of model complexity and accuracy. It is calculated with the number of nodes in the genetic programming tree, the order of the linear dynamic model and the accuracy of model for the training data. The results of numerical studies indicate the usefulness of proposed approach to Hammerstein model identification.