Abstract:

We propose three computationally efficient methods for finding optimal run curves of electrical trains, all based on the idea of approximating the continuous dynamics of a moving train by a Markov Decision Process (MDP) model. Deterministic continuous train dynamics are converted to stochastic transitions on a discrete model by observing the similarity between the properties of convex combinations and those of probability mass functions. The resulting MDP uses barycentric coordinates to effectively represent the cost-to-go of the approximated optimal control problem. One of the three solution methods uses equal distance steps, as opposed to the usual equal- time steps, to avoidself transitions of the MDP, which allows very fast computation of the cost-to-go in one pass only.