Fixed-time regulation control of uncertain nonholonomic systems and its applications

ABSTRACT

Stabilisation of nonholonomic systems is of great practical importance to the industry. Moreover, fixed-time control is more comfortable than finite-time control since the upper bound of the settling time is independent on the initial system states in a fixed-time control issue and therefore can be estimated in advance. Inspired by the aforementioned two points, we consider the fixed-time stabilisation for a kind of uncertain nonholonomic systems subject to perturbations in this paper. A globally fixed-time stabilisation strategy is proposed by taking advantage of adding one power integrator technique and switching ideal. Under the designed controllers, all states can be regulated to zero before a fixed time and kept zero afterwards. As an application, the fixed-time stabilisation for a class of dynamic nonholonomic systems is also addressed by the combined method of adding one power integrator and terminal sliding-mode control. Three mechanical and academic examples are provided to show the flexibility and effectiveness of the assumptions and control algorithms.

KEYWORDS:

• Nonholonomic systems
• nonlinear systems
• fixed-time stabilisation
• adding one power integrator
• terminal sliding mode (TSM)

Acknowledgements

The authors thank the editor and the anonymous reviewers for their constructive comments and suggestions for improving the quality of the paper.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was partially supported by the National Nature Science Foundation of China [grant number 61273091], [grant number 61403003]; the Project of Taishan Scholar of Shandong Province of China [grant number TS20120529]; the PhD Program Foundation of Ministry of Education of China [grant number 20123705110002]; and the Graduate Student Innovation Foundation of Jiangsu Province of China [grant number KYLX15_0116].