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Mathematical Problems in Engineering
Volume 2013 (2013), Article ID 873430, 14 pages
Research Article

Tuning of a TS Fuzzy Output Regulator Using the Steepest Descent Approach and ANFIS

Instituto Politécnico Nacional, SEPI-ESIME Zacatenco, Avenue IPN S/N, 07738 México, DF, Mexico

Received 15 March 2013; Accepted 27 May 2013

Academic Editor: Qingsong Xu

Copyright © 2013 Ricardo Tapia-Herrera et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The exact output regulation problem for Takagi-Sugeno (TS) fuzzy models, designed from linear local subsystems, may have a solution if input matrices are the same for every local linear subsystem. Unfortunately, such a condition is difficult to accomplish in general. Therefore, in this work, an adaptive network-based fuzzy inference system (ANFIS) is integrated into the fuzzy controller in order to obtain the optimal fuzzy membership functions yielding adequate combination of the local regulators such that the output regulation error in steady-state is reduced, avoiding in this way the aforementioned condition. In comparison with the steepest descent method employed for tuning fuzzy controllers, ANFIS approximates the mappings between local regulators with membership functions which are not necessary known functions as Gaussian bell (gbell), sigmoidal, and triangular membership functions. Due to the structure of the fuzzy controller, Levenberg-Marquardt method is employed during the training of ANFIS.