Identification of a class of non‐linear parametrically varying models

Abstract

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.

Modeling and Identification of Linear Parameter-Varying Systems

“…The estimation is accomplished via either a mixed linear/nonlinear procedure or by a separable least-squares approach. In the former case, the functional dependencies of the coefficients are identified through a neural-network approach while the linear part of the model is estimated by linear regression (Previdi and Lovera 2003. The approach is developed further in Previdi and Lovera (2004), where the parallel estimation problem of the neural-network model and the linear part is solved by a separable least-squares strategy.…”

Optimized Proportional-Integral-Derivative Control Strategies and Simulation for Lower Limb Functional Electrical Stimulation

“…The model used in this study was an advanced nonlinear autoregressive exogenous model where the "forward" part was given by conventional linear regression and the "feedback" part was represented by a nonlinear dynamic map parameterized by a neural network which can take into account more complex variables [9]. The structure of model is showed in Fig.1 The structure can be described by the following equation…”

Robust generation of LPV state-space models using a regularized &#x210C;<inf>2</inf>-cost

“…There are also methods that address the problem of preserving the input-output relation and try to generate an LPV-model using, e.g. linear regression [4] or nonlinear optimization [5]. An excellent survey of existing methods can be found in [6].…”