I. Introduction
Position and velocity tracking problem is one of the essential problems of the train operation control systems. In the context of automatic railway transportation systems, most existing methods for automatic train control are based on either the single-point-mass model [1], [2] or the multiple-point-mass model [3]–[12]. Based on the dynamic model of automatic train, various control issues of cargo and passenger trains have been studied in the recent years such as cruise control for high speed trains [4], input/output decoupling problem for high speed trains [5], optimal driving combined with a desired speed profile with energy consumption [8], and so on. However, all of these results assume the controller or actuator always works efficiently during the operation, and the actuator failures are rarely taken into account in those methods. In practice, the controller or actuator may lose its efficiency or even completely collapse during its operation, which brings great threats to the safety of high speed trains, thus it is necessary to introduce a reliable control strategy that is able to tolerate the failures of actuator and maintain the system stability and performance, which is the main purpose of this paper.