Mathematical Problems in Engineering
Volume 2012 (2012), Article ID 493715, 18 pages
Research Article

Dynamic Feedback Backstepping Control for a Class of MIMO Nonaffine Block Nonlinear Systems

Department of Control Engineering, Naval Aeronautical and Astronautical University, Yantai, Shandong 264001, China

Received 23 November 2011; Revised 26 January 2012; Accepted 4 April 2012

Academic Editor: Christos H. Skiadas

Copyright © 2012 Hai-Yan Li 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.


For a class of MIMO nonaffine block nonlinear systems, a neural network- (NN-) based dynamic feedback backstepping control design method is proposed to solve the tracking problem. This problem is difficult to be dealt with in the control literature, mainly because the inverse controls of block nonaffine systems are not easy to resolve. To overcome this difficulty, dynamic feedback, backstepping design, sliding mode-like technique, NN, and feedback linearization techniques are incorporated to deal with this problem, in which the NNs are used to approximate and adaptively cancel the uncertainties. It is proved that the whole closed-loop system is stable in the sense of Lyapunov. Finally, simulations verify the effectiveness of the proposed scheme.