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The Scientific World Journal
Volume 2014, Article ID 951983, 10 pages
http://dx.doi.org/10.1155/2014/951983
Research Article

Singularity-Free Neural Control for the Exponential Trajectory Tracking in Multiple-Input Uncertain Systems with Unknown Deadzone Nonlinearities

1Sección de Estudios de Posgrado e Investigación, ESIME UA-IPN, Avenida de las Granjas, No. 682, Colonia Santa Catarina, México, DF 02250, Mexico
2Departamento de Control Automático, CINVESTAV-IPN, Avenida Instituto Politécnico Nacional, No. 2508, México, DF 07360, Mexico

Received 27 February 2014; Accepted 21 May 2014; Published 19 June 2014

Academic Editor: Chin-Chia Wu

Copyright © 2014 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.

Abstract

The trajectory tracking for a class of uncertain nonlinear systems in which the number of possible states is equal to the number of inputs and each input is preceded by an unknown symmetric deadzone is considered. The unknown dynamics is identified by means of a continuous time recurrent neural network in which the control singularity is conveniently avoided by guaranteeing the invertibility of the coupling matrix. Given this neural network-based mathematical model of the uncertain system, a singularity-free feedback linearization control law is developed in order to compel the system state to follow a reference trajectory. By means of Lyapunov-like analysis, the exponential convergence of the tracking error to a bounded zone can be proven. Likewise, the boundedness of all closed-loop signals can be guaranteed.