Numerical Study on Dynamic Programming Applied to Optimization of Running Profile of a Train

Abstract

An algorithm, optimizing the train running profile with Bellman's Dynamic programming (DP), was discussed. An optimal train running trajectory which minimizes amount of total consumed energy, was produced under fixed origin and destination, limited electric motive force, stipulated running time and electric brake by VVVF controlled induction motor/generator blended with mechanical brake, several local speed constraints and local inclines. The position and velocity of train and total running time were divided into nonuniform lattice and the numerical algorithm solved state equations partially and calculated interpolated local valuation. The required error of distance and speed at destination is less than 0.6m and 0.1m/sec respectively.