Cooperative control and stability analysis for virtual coupling of rail vehicles

Cooperative control for rail vehicles is a new idea which builds on existing models and methods developed in the context of flight formation and autonomous ground vehicles. The underlying idea is to assimilate virtually coupled rail vehicles to arrays of mass-spring-dashpot systems. The contribution of this paper is three-fold. First, a novel scheme is proposed which involves a supervisory control for the higher-level planning and a local motion coordination for the lower-level implementation. For the supervisory control, a review of the existing scheduling models and methods based on alternate graphs and a mixed-integer (non)linear program is conducted. For the local coordination, a nonlinear and uncertain model is developed and a constructive method is provided to design a feedback control that stabilizes the vehicle around a desired equilibrium point, in terms of position and velocity. Second, the control design method is extended to the case of multiple virtually coupled vehicles. It is proven that the transient dynamics follows a typical synchronization dynamics. It is also proven that under such control, the whole system of rail vehicles converges to a pre-defined equilibrium point, characterized by a specific velocity and relative distance between vehicles. Conditions for the stability of such equilibrium points are investigated. Third, under the hypothesis of homogeneity, bounds on the damping coefficient for the synchronization equilibrium (in terms of velocity and relative distance between vehicles) to be overdamped or underdamped are provided.