Second-order sliding mode controller design with mismatched term and time-varying output constraint

Highlights：

• This is the first work to investigate the design of SOSM controller with mismatched uncertainty and time-varying output constraint, and to further verify the stability of the uncertain system.

• A new time-varying BLF has been constructed to handle the time-varying output constraint. By modifying the API technique and using the time-varying BLF, a SOSM controller for the SOSM dynamics under the time-varying output constraint is systematically projected such that the finite-time stability of closed-loop system can be guaranteed. Meanwhile, the time-varying output condition is never violated during operation.

• In accordance with the Lyapunov approach, the finite-time stability of the closed-loop sliding mode dynamics is confirmed. Notably, the proposed method can handle nonlinear systems with the time-varying output constraint, static symmetrical output constraint, and can also be used to deal with nonlinear systems without output constraint. Therefore, the SOSM controller which is developed in this paper is more general.

摘要

•This is the first work to investigate the design of SOSM controller with mismatched uncertainty and time-varying output constraint, and to further verify the stability of the uncertain system.•A new time-varying BLF has been constructed to handle the time-varying output constraint. By modifying the API technique and using the time-varying BLF, a SOSM controller for the SOSM dynamics under the time-varying output constraint is systematically projected such that the finite-time stability of closed-loop system can be guaranteed. Meanwhile, the time-varying output condition is never violated during operation.•In accordance with the Lyapunov approach, the finite-time stability of the closed-loop sliding mode dynamics is confirmed. Notably, the proposed method can handle nonlinear systems with the time-varying output constraint, static symmetrical output constraint, and can also be used to deal with nonlinear systems without output constraint. Therefore, the SOSM controller which is developed in this paper is more general.