Linear and non-linear system identification using separable least-squares

We demonstrate how the separable least-squares technique of Golub and Pereyra can be exploited in the identification of both linear and non-linear systems based on the prediction error formulation. The model classes to be considered here are the output error model and innovations model in the linear case and the Wiener system in the Pion-linear case. This technique together with a suitable choice of parametrisation allow us to solve, in the linear case, the associated optimisation problem using only np parameters instead of the usual n(m + p) + mp parameters when canonical forms are used, where n, m and p denote respectively the number of states, inputs and outputs, We also prove under certain assumptions that the separable optimisation method is numerically better conditioned than its non-separable counterpart. Successful operations of these identification algorithms are demonstrated by applying them to two sets of industrial data: an industrial dryer in the linear case and a high-purity distillation column in the non-linear case.