Mathematical Problems in Engineering
Volume 2012 (2012), Article ID 342739, 23 pages
Research Article

Robust Adaptive Neurocontrol of SISO Nonlinear Systems Preceded by Unknown Deadzone

1Centro Universitario de Ciencias Exactas e Ingenierías, Universidad de Guadalajara, Boulevord Marcelino García Barragán 1421, 44430 Guadalajara, JAL, Mexico
2Sección de Estudios de Posgrado e Investigación, ESIME UA-IPN, Avenida de las Granjas 682, Col. Santa Catarina, 02250 México DF, Mexico

Received 21 June 2012; Revised 6 August 2012; Accepted 16 August 2012

Academic Editor: Jung-Fa Tsai

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 this study, the problem of controlling an unknown SISO nonlinear system in Brunovsky canonical form with unknown deadzone input in such a way that the system output follows a specified bounded reference trajectory is considered. Based on universal approximation property of the neural networks, two schemes are proposed to handle this problem. The first scheme utilizes a smooth adaptive inverse of the deadzone. By means of Lyapunov analyses, the exponential convergence of the tracking error to a bounded zone is proven. The second scheme considers the deadzone as a combination of a linear term and a disturbance-like term. Thus, the estimation of the deadzone inverse is not required. By using a Lyapunov-like analyses, the asymptotic converge of the tracking error to a bounded zone is demonstrated. Since this control strategy requires the knowledge of a bound for an uncertainty/disturbance term, a procedure to find such bound is provided. In both schemes, the boundedness of all closed-loop signals is guaranteed. A numerical experiment shows that a satisfactory performance can be obtained by using any of the two proposed controllers.