In the European Rail Traffic Management System (ERTMS), the Route Control Centre System (RCCS) supervises the distance between consecutive trains and generates movement authorities, i.e. the permission for a train to move to a specific location within the constraints of the infrastructure and with supervision of speed. In this work, a control model aimed at determining the speed and position of a train platoon within a sector of the rail network is presented. The central controller, i.e. the RCCS, receives information about the current position and speed of trains and it sends them decisions about optimal corrective actions for each train. Priorities of trains are handled to respect the planned timetable, taking into account the train dynamics, limitations in divergences of positions, speeds, and tractive effort, as well as minimum distances between consecutive trains. The control approach is based on a quite innovative linear quadratic regulator allowing the definition of stochastic constraints. The validation of the model is based on data collected from a RCCS for a Section of the high-speed Paris-London line