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Mathematical Problems in Engineering
Volume 2016, Article ID 4085929, 11 pages
Research Article

Adaptive Neural Control of Nonaffine Nonlinear Systems without Differential Condition for Nonaffine Function

The College of Aeronautics and Astronautics Engineering, Air Force Engineering University, Xi’an 710038, China

Received 10 December 2015; Revised 4 May 2016; Accepted 16 May 2016

Academic Editor: Haranath Kar

Copyright © 2016 Chaojiao Sun 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.


An adaptive neural control scheme is proposed for nonaffine nonlinear system without using the implicit function theorem or mean value theorem. The differential conditions on nonaffine nonlinear functions are removed. The control-gain function is modeled with the nonaffine function probably being indifferentiable. Furthermore, only a semibounded condition for nonaffine nonlinear function is required in the proposed method, and the basic idea of invariant set theory is then constructively introduced to cope with the difficulty in the control design for nonaffine nonlinear systems. It is rigorously proved that all the closed-loop signals are bounded and the tracking error converges to a small residual set asymptotically. Finally, simulation examples are provided to demonstrate the effectiveness of the designed method.