Nonlinear dynamical system identification using reduced Volterra models with generalised orthonormal basis functions

Volterra models can be used to describe a wide class of nonlinear systems. However their practical use is limited due to the huge number of coefficients that need to be estimated even for simple SISO systems. Orthonormal basis functions, like distorted sine functions and Laguerre functions, have been proposed as a means to reduce the number of parameters. In linear system identification generalized orthonormal basis functions have been widely used to reduce the number of parameters one needs to estimate with very promising results. In this paper, we extend the use of generalized orthonormal basis functions to cover the nonlinear system identification and discuss the merits of such use. Finally, we give two examples on which we implement the proposed method, a CSTR system (SISO case) and a model IV fluid catalytic cracking unit (MIMO case).