Adaptive fuzzy fault-tolerant control for multiple high-speed trains with proportional and integral-based sliding mode

In this study, novel adaptive fuzzy fault-tolerant control method is proposed for multiple high-speed trains (HSTs) in the presence of actuator faults, unknown non-linear dynamics and external disturbances. The fuzzy logic system is used to approximate the unknown functions. Based on proportional and integral-based sliding mode technique, two adaptive fuzzy control schemes are then proposed to achieve string stability. In the first scheme, the actuator faults are not considered. In the second scheme, a novel fuzzy fault-tolerant control with fewer adjustable parameters is constructed to further reduce the online computational load. By using Lyapunov analysis, the individual stability and string stability of whole multiple HSTs are proven. In addition, all signals of the closed-loop system are uniformly ultimately bounded and all HSTs track the reference trajectory to a small compact set around zero. Finally, comparative simulation is introduced to verify the reliability and effectiveness.