Distributed constrained control for multi-train systems with multiple cars

In practical multi-train systems, there are four different kinds of necessary nonlinearities cause by the interactive forces between adjacent cars, the nonlinear resistances, the input constraints, and the velocity constraints. However, most of the existing works on distributed control for multi-train systems only focused one or two kinds of these nonlinearities. To the best of our knowledge, there are only a few works considering three kinds of these nonlinearities. In this paper, the effects of control input and velocity constraints, interactive forces between adjacent cars and the train running resistance on the system are studied, and a distributed cooperative control algorithm based on the state information of adjacent cars is proposed. The analysis is given based on model transformations, appropriate parameter selection and convex analysis. It is proved that all trains finally run in a given formation even when the inputs and velocities of all trains are constrained to lie in some given sets. Numerical simulation examples are presented to demonstrate the theoretical conclusions.