Adaptive neural control of non-affine pure-feedback non-linear systems with input nonlinearity and perturbed uncertainties

Abstract

In this article, two robust adaptive control schemes are investigated for a class of completely non-affine pure-feedback non-linear systems with input non-linearity and perturbed uncertainties using radial basis function neural networks (RBFNNs). Based on the dynamic surface control (DSC) technique and using the quadratic Lyapunov function, the explosion of complexity in the traditional backstepping design is avoided when the gain signs are known. In addition, the unknown virtual gain signs are dealt with using the Nussbaum functions. Using the mean value theorem and Young's inequality, only one learning parameter needs to be tuned online at each step of recursion. It is proved that the proposed design method is able to guarantee semi-global uniform ultimate boundedness (SGUUB) of all signals in the closed-loop system. Simulation results verify the effectiveness of the proposed approach.

Keywords:

• adaptive control
• neural networks
• dynamic surface control
• pure-feedback non-linear systems
• input non-linearity
• Nussbaum function

Acknowledgements

The authors would like to thank the referees for their helpful comments and suggestions. This study was partially supported by the National Natural Science Foundation of China (60874045 and 60904030 and 60774017) and the Natural Science Foundation of Jiangsu Province (BK2009184).