Multimodel System Identification Based on New Fuzzy Partitioning Similarity Measure
Abdelhadi Radouane1, Fouad Giri2, Abdessamad Naitali3, Fatima Zahra Chaoui4

1Abdelhadi Radouane*, RMI Lab, FST Hassan First University of Settat, Morocco.
2Fouad Giri, UNICAEN LAC Lab, Caen Normandie University, Caen, France.
3Abdessamad Naitali, M2PI Lab, ENSAM, Mohammed V University, Rabat, Morocco.
4Fatima Zahra Chaoui, M2PI Lab, ENSAM, Mohammed V University, Rabat, Morocco.

Manuscript received on June 26, 2021. | Revised Manuscript received on July 17, 2021. | Manuscript published on July 30, 2021. | PP: 19-30 | Volume-10, Issue-9, July 2021 | Retrieval Number: 100.1/ijitee.I92900710921 | DOI: 10.35940/ijitee.I9290.0710921
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Abstract: The problem of identifying unstructured nonlinear systems is generally addressed on the basis of multi-model representations involving several linear local models. In the present work, local models are combined to get a global representation using incremental fuzzy clustering. The main contribution is a novel vector similarity measure defined in the System Working Space (SWS) that combines the angular deviation and the usual Euclidean distance. Such a combination makes the new metric highly discriminating leading to a better partitioning of the operating space providing, thereby, a higher accuracy of the model. The developed partitioning method is first evaluated by performing linear local model (LLM) based identification of a academic benchmark multivariable nonlinear system. Then, the performances of the identification method are evaluated using experimental tropospheric ozone data. These evaluations illustrate the supremacy of the new method over the standard Euclidian-distance based partitioning approach. 
Keywords: MIMO Nonlinear Systems, System Identification, Local Linear Models, Fuzzy Clustering, Similarity Measure, Angular Deviation, Weighted Least-Squares (WLS).