Fixed-time stabilisation for switched stochastic nonlinear systems with asymmetric output constraints

Abstract

In this paper, the fixed-time stabilisation problem is investigated for switched stochastic nonlinear systems with asymmetric output constraints. A novel universal barrier Lyapunov function is proposed to not only handle systems with asymmetric output constraints but also work for systems with symmetric constraints or without constraints, without reshaping the controller framework. On the basis of the stochastic fixed-time stability theorem and adding a power integrator strategy, an elaborate control method is established to ensure that the system state fixed-time converges to zero almost surely without the knowledge of initial conditions. Meanwhile, the system output is always retained in the preset asymmetric region in probability. A practical example is utilised to verify the validity of the proposed theory.

Keywords:

• Asymmetric output constraints
• fixed-time stability
• switched stochastic nonlinear systems
• adding a power integrator

Acknowledgements

This work was supported in part by National Natural Science Foundation of China (No. 61903232).

Disclosure statement

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

Additional information

Funding

This work was supported in part by National Natural Science Foundation of China [grant number 61903232].

Notes on contributors

Zhibao Song

Zhibao Song received his B.S. degree at School of Mathematics and Statistics, Taishan University, in 2012, M.S. degree at School of Engineering, Qufu Normal University, in 2015 and Ph.D. degree at School of Automation, Southeast University, in 2018. He is currently a lecturer at College of Mathematics and Systems Science, Shandong University of Science and Technology. His research interests include time-delay systems, switched control, stochastic systems and adaptive control.

Ping Li

Ping Li received her Ph.D. degree in School of Automation, Nanjing University of Science and Technology in 2018. She is currently a lecture in School of Mathematics and Systems Science, Shandong University of Science and Technology. From November 2016 to April 2017, she was a joint supervisory Ph.D. student in Department of Electrical and Computer Engineering, Dalhousie University. Her research interests include adaptive control, finite-time control for nonlinear systems and multi-agent systems.