Distributed Bang–Bang Control for Multitrain Systems With Self-Adjusting Zones and Communication Delays

In real applications, the expected distances between adjacent trains are usually not fixed values, but some specific intervals called “self-adjusting zones” in this article. This article is devoted to address the cooperative control problem of multitrain systems with self-adjusting zones, constraints, communication delays, and collision avoidance. To enhance the rapidity of the systems, a distributed bang–bang control algorithm is introduced with communication delays. It is shown that all trains will eventually achieve stable operation with a desired velocity while remaining in the self-adjusting zones in the absence of communication delays or remaining in the neighborhood of the self-adjusting zones in the presence of communication delays. The analysis is mainly based on linear equivalent transformations of the sign functions and constraints, and the convexity of stochastic matrices. Finally, numerical examples show the effectiveness of the proposed algorithm.