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Mathematical Problems in Engineering
Volume 2015, Article ID 198371, 18 pages
http://dx.doi.org/10.1155/2015/198371
Research Article

Synchronization of Discrete-Time Chaotic Fuzzy Systems by means of Fuzzy Output Regulation Using Genetic Algorithm

1Instituto Politécnico Nacional, SEPI-ESIME Zacatenco, Avenida IPN S/N, 07738 México, DF, Mexico
2Instituto Politécnico Nacional, SEPI-ESIME Azcapotzalco, Avenida de las Granjas No. 682, 02250 Azcapotzalco, México, DF, Mexico

Received 7 August 2015; Accepted 4 November 2015

Academic Editor: Rongwei Guo

Copyright © 2015 Tonatiuh Hernández Cortés 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.

Abstract

The synchronization of chaotic systems, described by discrete-time T-S fuzzy models, is treated by means of fuzzy output regulation theory. The conditions for designing a discrete-time output regulator are given in this paper. Besides, when the system does not fulfill the conditions for exact tracking, a new regulator based on genetic algorithms is considered. The genetic algorithms are used to approximate the adequate membership functions, which allow the adequate combination of local regulators. As a result, the tracking error is significantly reduced. Both the Complete Synchronization and the Generalized Synchronization problem are studied. Some numerical examples are used to illustrate the effectiveness of the proposed approach.