ELM-based adaptive backstepping neural control for a class of uncertain MIMO nonlinear systems with predefined tracking accuracy

Abstract

In this work, the adaptive backstepping neural control technique is proposed for a class of uncertain multi-input multi-output nonlinear systems in block-triangular form with the ultimate tracking accuracy assumed to be known a priori. The stability analysis of the closed-loop control system is derived based on Barbalat's Lemma instead of Lyapunov stability theory. Semi-global uniform ultimate boundedness of all the signals in the closed-loop system is achieved and after a sufficiently large interval of time, the outputs of the system are proven to converge to the predefined value. A single hidden layer feed-forward neural network based on the extreme learning machine is used in this work to approximate the unknown nonlinear functions in the control laws. Two simulation examples, including a mathematical one and a practical one, are given to verify the effectiveness of the proposed controller and its superiority over the existing techniques.

Keywords:

• MIMO nonlinear system
• adaptive backstepping design
• ELM-based SLFNN
• Barbalat's Lemma

Acknowledgements

This work is supported by the National Natural Science Foundation of China (61174213), the Program for New Century Excellent Talents in University (NCET-10-0665) and the National Basic Research Program (973 Program) of China (No. 2013CB329402).