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Mathematical Problems in Engineering
Volume 2013, Article ID 520390, 14 pages
Research Article

Adaptive Stabilization for Nonholonomic Systems with Unknown Time Delays

1College of Electric and Information Engineering, Zhengzhou University of Light Industry, Zhengzhou, Henan 450002, China
2Department of Mathematics, Southeast University, Nanjing, Jiangsu 210096, China
3Department of Mathematics and Information Science, Zhengzhou University of Light Industry, Zhengzhou, Henan 450002, China
4Research Institute of Automation, Qufu Normal University, Qufu, Shandong 273165, China

Received 19 June 2013; Revised 20 October 2013; Accepted 3 November 2013

Academic Editor: Oleg V. Gendelman

Copyright © 2013 Yuanyuan Wu 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 presents an adaptive control strategy for a class of nonholonomic systems in chained form with virtual control coefficients, nonlinear uncertainties, and unknown time delays. State scaling technique and backstepping recursive approach are applied to design a nonlinear state feedback controller, which can guarantee the stabilization of the closed-loop systems. The simulation results are provided to show the effectiveness of the proposed method.