Identification of a class of non-linear parametrically varying models

Previdi F., M. Lovera

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.

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