Cooperative control for multiple train systems: Self-adjusting zones, collision avoidance and constraints

In practical multiple train systems, the desired relative positions of adjacent trains are usually not fixed values but some certain zones which are called “self-adjusting zones” in this paper. However, most of the existing related works were concerned about the case of fixed values and few works focused on the more practical case when the desired relative positions are some certain zones. The aim of this paper is to investigate cooperative control for multiple train systems under moving block system by taking into account self-adjusting zones, collision avoidance and constraints simultaneously, where each train needs not to coordinate with other trains in its desired self-adjusting zones and can be self-adjusted freely. A distributed cooperative control algorithm is proposed to enable all trains to track the desired velocity and operate steadily in their self-adjusting zones by only utilizing the local information of neighbor trains, where a switching mechanism is introduced to ensure the trains to avoid collision. The analysis is performed mainly based on the properties of stochastic matrices and multiple model transformations. It is shown that the braking process can be equivalent to a special coordination process, and the braking process, the coordination process and the self-adjusting process can be unified as an integrated whole to be analyzed by using the properties of stochastic matrices. By addressing the state interactions of the train equivalent system under different scenarios, it is proved that all relative positions of adjacent trains converge into desired self-adjusting zones without the occurrence of collision, while all trains finally move in a desired velocity. Numerical examples are included to illustrate the obtained results.