Nonlinear system identification for control using Volterra-Laguerre expansion

The large number of parameters needed to represent the kernels is the major criticism in using Volterra series as nonlinear models. Kurth and Rake (1994) proposed a scheme to reduce this number for Hammerstein and Wiener systems. In this paper, the authors extend this scheme to general nonlinear systems and investigate the conditions under which a nonlinear system can be represented by the Volterra-Laguerre expansion. It is found that systems which possess such expansion can be characterized by the concept of stably separable kernels. As such, a large class of systems of practical interest, like fading memory nonlinear systems, can be approximated by the Volterra-Laguerre expansion. An orthogonal regression analysis method is introduced to further reduce the parameter number. The control-relevant identification issue pertinent to high performance nonlinear internal model control (NIMC) is accordingly addressed in the CSTR and rapid thermal processing (RTP) examples are provided to illustrate the usefulness of this technique