Multi-model identification of a fractional non linear system

Takagi-Sugeno fuzzy models have proved to be a powerful tool for non-linear system identification. Due to their simplicity, linear integer sub-models are mainly used in such structure. In this paper multi-model approach, based on Takagi-Sugeno form is used to perform identification of fractional non-linear systems, applying fractional local models. In this purpose, an output error method is used, and the algorithm is extended to the fractional case. Numerical simulations are performed in order to analyze the two sub-models: integer and fractional, fitting ability to approximate the non linear system behaviour. The validation of the method is carried out on real data of the heat diffusion.