Parameter-dependent sliding mode control for Markovian jump systems within finite-time interval: handling randomly occurring actuator faults

Abstract

In this article, the finite-time sliding mode control problem is studied for the Markovian jump systems. The uncertainties and actuator faults are randomly occurring and varying, which are simultaneously considered in the controlled systems. In order to characterise the stochastic phenomenon, two independent exponentials distributed random variables are introduced. To implement finite-time control performance, a suitable sliding mode controller is developed, which forces the trajectories of the system onto the specified sliding surface in a given finite-time (possibly short) interval. Besides, sufficient conditions are obtained to guarantee the stochastic finite-time boundedness within the entire finite-time interval, including the reaching and the sliding motion phases. Finally, simulation results demonstrate the feasibility of the proposed control strategy.

Keywords:

• Markovian jump systems
• stochastic finite-time boundedness
• sliding mode control
• random uncertainties
• actuator faults

Acknowledgements

This work was supported in part by the NNSF (62073139).

Disclosure statement

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

Additional information

Funding

This work was supported in part by the National Natural Science Foundation of China (NNSF) [grant number 62073139].

Notes on contributors

Meng Zhao

Meng Zhao received the B.S. degree in mathematics and applied mathematics and the M.S. degree in applied mathematics from Bohai University, Jinzhou, China, in 2014 and 2018, respectively. She is currently pursuing the Ph.D. degree with the East China University of Science and Technology, China. Her current research interests include sliding mode control, Markovian jump systems, and finite-time stability.

Yugang Niu

Yugang Niu received the M.Sc. and Ph.D. degrees in control engineering from the Nanjing University of Science and Technology, Nanjing, China, in 1992 and 2001, respectively. In 2003, he joined the School of Information Science and Engineering, East China University of Science and Technology, Shanghai, China, where he is currently a Professor. His research Areas includes sliding mode control, Markov jumping system, wireless sensor networks, micro grid.