Two-Stage Predefined-Time Exact Sliding Mode Control Based on Predefined-Time Exact Disturbance Observer

This paper is concerned with the predefined-time exact sliding mode control issue of a class of high-order uncertain nonlinear systems with disturbances. The proposed control scheme is composed of a predefined-time exact disturbance observer and a two-stage predefined-time exact sliding mode controller. The disturbance observer can estimate the system disturbances accurately within an arbitrary predefined observation time, and the time can be set as the handover time between two control stages. The classic sliding mode controller guarantees bounded system states in the first control stage. Then, a predefined-time sliding mode controller is designed based on time-varying tuning function, regulating the system states to exact zero within a final predefined settling time in the second stage. It is shown that the control input signal is always chattering-free with respect to time. The effectiveness and superiority of the proposed control scheme is demonstrated with simulation examples.