Minimum energy trajectories for subway systems

The problem of determining the tunnel trajectory together with an optimal control policy of a train in subway systems is addressed in this paper. The cost function chosen in this study is the total energy consumed by a train in a round trip. Several constraints such as maximum velocity, maximum slopes, maximum acceleration, maximum electrical force and so on, as well as a relatively simple model of the train are considered. The solution is obtained by using the Gradient-Restoration method developed by Angelo Miele et al. An application considering the kind of trains existing in the Santiago subway is presented and the results are compared with the existing tunnel profile from an energy consumption viewpoint. Important energy savings are obtained due to differences in proposed and existing tunnels, assuming that in both cases the operation policy is the same (optimal for a given tunnel).