Journal of Applied Mathematics
Volume 2012 (2012), Article ID 529176, 20 pages
Research Article

System Identification Using Multilayer Differential Neural Networks: A New Result

1Centro Universitario de Ciencias Exactas e Ingenierías, Universidad de Guadalajara, Boulevard Marcelino García Barragán No. 1421, 44430 Guadalajara, JAL, Mexico
2Sección de Estudios de Posgrado e Investigación, ESIME-UA, IPN, Avenida de las Granjas No. 682, 02250 Santa Catarina, NL, Mexico

Received 22 November 2011; Revised 30 January 2012; Accepted 2 February 2012

Academic Editor: Hector Pomares

Copyright © 2012 J. Humberto Pérez-Cruz 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.


In previous works, a learning law with a dead zone function was developed for multilayer differential neural networks. This scheme requires strictly a priori knowledge of an upper bound for the unmodeled dynamics. In this paper, the learning law is modified in such a way that this condition is relaxed. By this modification, the tuning process is simpler and the dead-zone function is not required anymore. On the basis of this modification and by using a Lyapunov-like analysis, a stronger result is here demonstrated: the exponential convergence of the identification error to a bounded zone. Besides, a value for upper bound of such zone is provided. The workability of this approach is tested by a simulation example.