Time-optimal tracking control of trains using Pontryagin's maximum principle

The advancement of control and communication technology has made it possible to realize moving blocking in rail system. To guarantee the operational safety of trains, moving blocking requires the distance between any two adjacent trains should always keep greater than a predetermined length. In this sense, the latter train can brake within the determined distance even if the front train stopped due to uncertain reasons. Therefore, to improve the operational efficiency of rail system, it is necessary to control the length of adjacent trains to the security length as fast as possible. By using Pontryagin's maximum principle, this paper gives a control strategy which can make the latter train approach the front train with the minimal traveling time, while keeping their distance greater the security length.