The use of the multimodd approach in the modelling, analysis and control of non-linear complex and/or ill-defined systems was advocated by many researchers. This approach supposes the definition of a set of local models valid in a given region or domain. Different strategies exist in the literature and are generally based on a partitioning of the non-linear system's full range of operations into multiple smaller operating regimes, each of which is associated with a locally valid model or controller. However, most of these strategies, which suppose the determination of these local models as weII as their validity domain. remain arbitrary and are generally fixed thanks to certain a priori knowledge of the system. Meanwhile, the transition problem between the different models, which may use either a simple commutation or a fusion technique is stiil pending. The purpose of this paper is to propose a new approach to derive a multimodel base allowing us to limit the number of models in the base to four models. Besides, a fuzzy fusion technique is presented and has the following main advantages: (i) use of a fuzzy partitioning in order to determine the validity of each model which enhances the robustness of the solution; (ii) introduction, besides the four extreme models, of another model, called average model, determined as an average of the boundary models. The theoretical study is validated by simulation and a robustness analysis is carried out under particularly severe conditions.
Multimodel approach, validity domain, futzzy fusion, Kharitonov criteria
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