Prescribed-time stabilisation design for a class of nonlinear systems with state constraints

Abstract

This paper will investigate the prescribed-time stabilisation problem for a class of nonlinear systems with state constraints. A recursive design algorithm is proposed to solve the prescribed-time stabilisation problem. Firstly, a barrier Lyapunov function (BLF) is employed and a time-varying coordinate transformation is utilised. Then, a modified method of $L_{g}V$-backstepping is proposed, and a novel stabilising function by adding a fractional term proposed in this paper which is capable of decreasing the BLF to the origin within any desired settling time and then achieving the prescribed-time stabilisation. Such a fractional term plays an important role in achieving prescribed-time stabilisation. Next, the analysis of the prescribed-time stabilisation with state constraints is presented. Finally, an example shows the effectiveness of the proposed method. The feature of this paper is that the settling time is not only independent of the design parameters, nor does it depend on the initial conditions, and can be set according to per our will. Other is that the constraints of all the states are not violated.

Keywords:

• Nonlinear systems
• $L_{g}V$-backstepping
• prescribed-time
• state constraints

Disclosure statement

No potential conflict of interest was reported by the author(s).

Data availability statement

Data sharing is not applicable to this article as no new data were created or analysed in this study.

Additional information

Funding

This work of Ruicheng Ma was partially supported by National Natural Science Foundation of China [grant number 62073157] and Natural Science Foundation of Liaoning province [grant number 2022-MS-173].

Notes on contributors

Siqi Wang

Siqi Wang received her B.S. degree in Information and Computing Science from Liaoning University of Technology, Jinzhou, China, in 2020. She is now working towards the M.S. degree in Operational Research and Cybernetics from Liaoning University, Shenyang, China. Her research interests include switched systems and nonlinear systems.

Ruicheng Ma

Ruicheng Ma received his M.S. degree in Applied Mathematics from Liaoning University, Shenyang, China, in 2008. He completed his Ph.D. in Control Theory and Control Engineering from Northeastern University, Shenyang, China, in 2012. He is currently a professor with the School of Mathematics and Statistics, Liaoning University, Shenyang, China. His research interests include switched systems, hybrid control, and nonlinear systems. He won the 2020 National Natural Science Award of China. He is currently an Editor of Control Engineering of China.