Terminal Time Regulator-Based Prescribed Performance Sliding-Mode Control

This paper proposes a prescribed performance sliding mode control method based on the terminal time regulator (TTRPPSMC), which enables the system state to converge into a predetermined region at a prescribed time instant, where both the convergence region and convergence time are arbitrary constants that can be given in advance. Firstly, a performance function that can be arbitrarily adjusted is constructed, and the nominal control is designed to ensure that the newly designed system state without disturbances strictly tracks the performance function trajectory and converges to zero at a prescribed time instant. Second, the discontinuous control based on the asymmetric barrier function is designed to ensure that the errors between the actual system state and the tracking trajectory always remain inside the prescribed performance function. Compared to traditional prescribed performance methods, the TTRPPSMC designed in this paper can determine the convergence time, steady-state accuracy, and overshoot of the system simultaneously. Moreover, the controller has a simple structure with few parameters, which are easy to tune. Finally, a comparative simulation with traditional prescribed performance methods is carried out. The proposed TTRPPSMC is also applied to the vehicle platoon system for the simulation to demonstrate the effectiveness of the designed control.