Multimodel control using fuzzy fusion

The use of the multimodel approach in modelling, analysis and control of non-linear complex and/or ill-defined systems has been 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 operation 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 well as their validity domain, remain arbitrary and are generally fixed thanks to a certain a priori knowledge of the system whatever its order. We recently proposed a new approach to derive a multimodel basis which allows us to limit the number of models in the basis to almost four models. Meanwhile, the transition problem between the different models, which may use either a simple commutation or a fusion technique, may still arise. In this paper, a fuzzy fusion technique is presented with the following main advantages: use of a fuzzy partitioning in order to determine the validity of each model which enhances the robustness of the solution; introduction of, besides the four extreme models, another model, called the average model, determined as an average of the boundary models. The theoretical study is validated by experimental results.