Distributed Constrained Tracking Control of Continuous-Time Multi-Train Systems With Self-Adjusting Zones and Delays

In practical multi-train systems, it is not necessary for the desired relative distances between adjacent trains to remain fixed. Instead, trains only need to converge within specific zones, where they can adjust their own velocity without coordination. This paper investigates distributed tracking control for multi-train systems considering communication delays, self-adjusting zones, and constraints on velocity and input simultaneously. A distributed algorithm is proposed to drive each train into its self-adjusting zone while tracking the desired velocity. It is shown that collision avoidance and velocity constraints can be achieved through velocity damping feedback. The research methods adopted in this paper mainly include multiple model transformations and convex analysis. By analyzing the equivalent system, it is demonstrated that tracking control is achievable for multi-train systems with constraints, continuous-time dynamics, communication delays, and self-adjusting zones. Finally, numerical simulations are conducted to verify the effectiveness of the theoretical findings.