A unified control approach to finite-time stabilization of SOSM dynamics subject to an output constraint

Abstract

This paper investigates a control design problem for the second-order sliding mode (SOSM) dynamics with mismatched uncertainty subject to the output constraint by means of the adding a power integrator technique. Firstly, a SOSM dynamics with mismatched uncertainty is constructed by retaining some information in the mismatched channel so as to reduce the uncertainty in the control channel, thereby relaxing the control requirement. Secondly, a barrier Lyapunov function (BLF) is designed in consideration of the output constraint to prevent the considered system from escaping from the output constraint. Moreover, the output constraint can be either symmetric or asymmetric. Thirdly, by embedding the above BLF into the adding a power integrator technique, a SOSM controller can be eventually constructed for the SOSM dynamics with the mismatched uncertainty to solve the output constraint problem. The finite-time stability analysis is proved by Lyapunov theory. The simulation results considering the symmetric constraint as well as the asymmetric constraint are provided to demonstrate the validity of the proposed control method.