Identification of structurally constrained second-order Volterra models

Continuing advances in industrial control hardware and software have increased interest in the identification of nonlinear dynamic models from chemical process data. Two practically important issues are those of nonlinear model structure selection and input sequence design for adequate model identification. While the “general nonlinear model identification problem” is intractably complex, we may obtain useful insights into both of these issues by restricting our attention to special cases, building incrementally on our “linear intuition”. We consider the special case of second-order Volterra models, focusing on the effects of structural restrictions and non-Gaussian input sequences on the model identification problem. The results presented build on the work of Powers and his co-workers, who considered the unconstrained Gaussian problem, certain constrained special cases (e.g., the Hammerstein model), and identification using non-i.i.d. input sequences. Besides extending these results to a wider class of model structure constraints and input sequences, the results presented yield some useful insights into the issue of input sequence design