Nonlinear system identification using heterogeneous multiple models
Résumé
Multiple models are recognised by their abilities to accurately describe nonlinear dynamic behaviours of a wide variety of nonlinear systems with a tractable model in control engineering problems. Multiple models are built by the interpolation of a set of submodels according to a particular aggregation mechanism, among them heterogeneous multiple model is of particular interest. This multiple model is characterized by the use of heterogeneous submodels in the sense that their state spaces are not the same and consequently they can be of various dimensions. Thanks to this feature, the complexity of the submodels can be well adapted to the complexity of the nonlinear system introducing flexibility and generality in the modelling stage. This paper deals with the off-line identification of nonlinear systems based on heterogeneous multiple model. Three optimisation criteria (global, local and combined) are investigated to obtain the submodel parameters according to the expected modelling performances. Particular attention is paid to the potential problems encountered in the identification procedure with a special focus on an undesirable phenomenon called no output tracking effect. The origin of this problem is explained and an effective solution is suggested to overcome this problem in the identification task. The abilities of this model are finally illustrated via relevant identification examples showing the effectiveness of the proposed methods.
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