Adaptive control under arbitrary switching for a class of switched nonlinear systems with nonlinear parameterisation

Abstract

This paper is devoted to discuss arbitrarily switching control problem for a class of nonlinearly parameterised nonlinear switched systems. Compared with the existing results, improvements are that a systematic procedure is given for an explicit construction of a common smooth adaptive controller independent of the switching signals. Meanwhile, the developed design method can be extended to the adaptive arbitrarily switching stabilisation problem for a class of cascade switched nonlinear systems. The theoretical analysis is presented for the Lyapunov stability of the resulting closed-loop switched system and the convergence of the original switched system states at the equilibrium under arbitrary switching. Moreover, the effectiveness and feasibility of the developed method are demonstrated by both a numerical example and a chemical system.

Keywords:

• switched system
• common Lyapunov function
• arbitrary switching
• adaptive control
• nonlinear parameterisation

Acknowledgements

This work is supported by the PhD Programs Foundation of Ministry of Education of China under Grant 20111333110001 and the Science and Engineering Foundation(B) for the young teachers of Yanshan University, China, under Grant 14LGB026. The authors also greatly appreciate the positive and constructive comments and suggestions from the editor and the anonymous reviewers, which have helped to improve the presentation of the paper.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

PhD Programs Foundation of Ministry of Education of China under [grant number 20111333110001]; The Science and Engineering Foundation(B) for the young teachers of Yanshan University, China [grant number 14LGB026].