Identification of piecewise affine systems by means of fuzzy clustering and competitive learning

This paper presents an identification method for a class of dynamic system known as piecewise affine systems. Such systems are composed of a set of affine maps which relate inputs and outputs. These maps are defined in disjunctive regions in the regression space, itself composed of system inputs and outputs.The aim of the proposed method is to obtain a model of the system from a set of input–output data. This model comprises a set of submodels defined in different regions of the regression space. The proposed method is sequenced according to several stages which identify the set of submodels and the regions in which they are defined. These submodels are obtained by means of an algorithm inspired by competitive learning which rewards those that best fit the data in each region of the regression space.The method uses a process of fuzzy clustering in order to obtain a subset of representatives from the original data set, so reducing the amount of information to be processed while retaining the significant information from the original data and minimizing the effect of noise on the data.