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Mathematical Problems in Engineering
Volume 2015 (2015), Article ID 519090, 7 pages
Research Article

Terminal Sliding Mode Control with Adaptive Law for Uncertain Nonlinear System

1School of Computer Science and Software Engineering, Tianjin Polytechnic University, Tianjin 300387, China
2School of Textiles, Tianjin Polytechnic University, Tianjin 300387, China
3Tianjin Vocational Institute, Tianjin 300410, China

Received 1 February 2015; Revised 16 April 2015; Accepted 20 April 2015

Academic Editor: Xinggang Yan

Copyright © 2015 Zhanshan Zhao 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.


A novel nonsingular terminal sliding mode controller is proposed for a second-order system with unmodeled dynamics uncertainties and external disturbances. We need not achieve the knowledge for boundaries of uncertainties and external disturbances in advance. The adaptive control gains are obtained to estimate the uncertain parameters and external disturbances which are unknown but bounded. The closed loop system stability is ensured with robustness and adaptation by the Lyapunov stability theorem in finite time. An illustrative example of second-order nonlinear system with unmodeled dynamics and external disturbances is given to demonstrate the effectiveness of the presented scheme.