Identification of a class of non-linear parametrically varying models

The aim of this paper is to propose a novel class of non-linear, possibly parameter-varying models suitable for system identification purposes. These models are given in the form of a linear fractional transformation (LFT) where the 'forward' part is represented by a conventional linear regression and the 'feedback' part is given by a non-linear dynamic map parameterized by a neural network (NN) which can take into account scheduling variables available for measurement. For this specific model structure a parameter estimation procedure has been set up, which turns out to be particularly efficient from the computational point of view. Also, it is possible to establish a connection between this model class and the well known class of local model networks (LMNs): this aspect is investigated in the paper. Finally, we have applied the proposed identification procedure to the problem of determining accurate non-linear models for knee joint dynamics in paraplegic patients, within the framework of a functional electrical stimulation (FES) rehabilitation engineering project.