A method to identify hybrid systems with mixed piecewise affine or nonlinear models of Takagi-Sugeno type

A clustering-based method to identify models that are piecewise affine or of Takagi-Sugeno type is presented. As prototype-based clustering algorithms, which are well suited for partitioning, frequently converge to unwanted local solutions, density-based noise clustering is used to initialize them. The clustering acts in a mixed parameter-position feature space and divides the data into separate sets for identifying local models and partition boundaries, which are assumed to be piecewise planar. The obtained partitions are tested on linearity and otherwise replaced each by a TS model that is identified from the respective data. The method is demonstrated for a test problem that includes switching, local polynomial nonlinearity as well as non-convex partition boundaries.