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In this paper, a novel adaptive fault-tolerant slidingmode control scheme is proposed for high-speed trains, where the longitudinal dynamical model is focused, and the disturbances and actuator faults are considered. Considering the disturbances in traction force generated by the traction system, a dynamic model with actuator uncertainties modelled as input distribution matrix uncertainty is established. Then, a new sliding-mode controller with design conditions is proposed for the healthy train system, which can drive the tracking error dynamical system to a pre-designed sliding surface in finite time and maintain the sliding motion on it thereafter. In order to deal with the actuator uncertainties and unknown faults simultaneously, the adaptive technique is combined with the fault-tolerant slidingmode control design together to guarantee that the asymptotical convergence of the tracking errors is achieved. Furthermore, the proposed adaptive fault-tolerant sliding-mode control scheme is extended to the cases of the actuator uncertainties with unknown bounds and the unparameterized actuator faults. Finally, case studies on a real train dynamic model are presented to explain the developed fault-tolerant control scheme. Simulation results show the effectiveness and feasibility of the proposed method.Index Terms-Actuator faults, fault-tolerant sliding-mode control, adaptive control, actuator uncertainty, high-speed train.

In this paper, an observer-based fault-tolerant control (FTC) method is proposed for a class of networked control systems (NCSs) with transfer delays. Markov chain is employed to characterize the transfer delays. Then, such kind of networked control systems are modelled as markovian jump systems. An observerbased FTC scheme using the delayed state information and the estimated fault value is presented to guarantee the stability of the faulty systems. An inverted pendulum example is used to illustrate the efficiency of the proposed method.