Spatio-Temporal Modeling for Hammerstein Distributed Parameter Systems

Abstract

A spatio-temporal Hammerstein modeling approach is presented in this chapter. To model the nonlinear distributed parameter system (DPS), a spatio-temporal Hammerstein model (a static nonlinearity followed by a linear DPS) is constructed. After the time/space separation, it can be represented by the traditional Hammerstein system with a set of spatial basis functions. To achieve a low-order model, the Karhunen-Loeve (KL) method is used for the time/space separation and dimension reduction. Then a compact Hammerstein model structure is determined by the orthogonal forward regression, and their unknown parameters are estimated with the least-squares method and the singular value decomposition. The simulation and experiment are presented to show the effectiveness of this spatio-temporal modeling method.