Universal stabilisation design for uncertain nonlinear system with sign-switching unknown control direction

Abstract

A universal robust control approach is proposed to stabilise a class of nonlinear systems. The system contains both nonlinear dynamics uncertainty and an unknown control direction, which is the multiplier of the control term. Being different from most previous studies, the unknown control direction is allowed to switch its sign in this article. A new Nussbaum gain technique is designed and integrated with robust controller to tackle the sign-switching unknown control direction. It is proven that the proposed control approach can yield asymptotic stabilisation and guarantee the boundedness of the closed-loop signals. In addition, these results can be readily extended to tracking problems under a different assumption.

Keywords:

• robust control
• uncertain nonlinear system
• control direction
• Nussbaum gain

Acknowledgements

This work was supported by grants from the National High-Tech Research and Development Program of China (No. 2012AA011602), the National Natural Science Foundation of China (No. 61004057, 61001172 and 61061130563), and the Specialised Research Fund for the Doctoral Program of China (No. 20100101110066).