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Abstract and Applied Analysis
Volume 2012, Article ID 471281, 18 pages
Research Article

Tracking Control Based on Recurrent Neural Networks for Nonlinear Systems with Multiple Inputs and Unknown Deadzone

1Centro Universitario de Ciencias Exactas e Ingenierías, Universidad de Guadalajara, Bulevar 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, Colonia Santa Catarina, 02250 Mexico City, DF, Mexico

Received 31 August 2012; Accepted 9 November 2012

Academic Editor: Wenchang Sun

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.


This paper deals with the problem of trajectory tracking for a broad class of uncertain nonlinear systems with multiple inputs each one subject to an unknown symmetric deadzone. On the basis of a model of the deadzone as a combination of a linear term and a disturbance-like term, a continuous-time recurrent neural network is directly employed in order to identify the uncertain dynamics. By using a Lyapunov analysis, the exponential convergence of the identification error to a bounded zone is demonstrated. Subsequently, by a proper control law, the state of the neural network is compelled to follow a bounded reference trajectory. This control law is designed in such a way that the singularity problem is conveniently avoided and the exponential convergence to a bounded zone of the difference between the state of the neural identifier and the reference trajectory can be proven. Thus, the exponential convergence of the tracking error to a bounded zone and the boundedness of all closed-loop signals can be guaranteed. One of the main advantages of the proposed strategy is that the controller can work satisfactorily without any specific knowledge of an upper bound for the unmodeled dynamics and/or the disturbance term.