Identification of Time-Varying Hammerstein Systems using a Basis Expansion Approach

The Hammerstein model is one of the simplest nonlinear system representations. It consists of a static nonlinear block in series with a dynamic linear block. This paper gives an identification method for time-varying Hammerstein systems: Hammerstein systems in which the parameters of the linear and nonlinear blocks vary as functions of time. The algorithm involves the expansion of the system's time-varying parameters onto finite sets of basis sequences thereby transforming the identification problem into a time-invariant one with respect to the expansion coefficients. Prediction error minimization is then carried out using a separable least squares algorithm to simplify computation and improve numerical conditioning. Results obtained from a simulation study of a time-varying Hammerstein system are presented to demonstrate the performance of the algorithm