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

We demonstrate how the separable least-squares technique of Golub and Perey ra can be exploited in the identification of both linear and non-linear sys tems based on the prediction error formulation. The model classes to be con sidered here are the output error model and innovations model in the linear case and the Wiener system in the Pion-linear case. This technique togethe r with a suitable choice of parametrisation allow us to solve, in the linea r case, the associated optimisation problem using only np parameters instea d of the usual n(m + p) + mp parameters when canonical forms are used, wher e n, m and p denote respectively the number of states, inputs and outputs, We also prove under certain assumptions that the separable optimisation met hod is numerically better conditioned than its non-separable counterpart. S uccessful operations of these identification algorithms are demonstrated by applying them to two sets of industrial data: an industrial dryer in the l inear case and a high-purity distillation column in the non-linear case.