Energy-Efficient Train Control Based on Improved Dynamic Programming Algorithm for Online Applications

The optimization algorithm for Energy Efficient Train Control (EETC) must meet train operation's safety, punctuality, and energy-saving characteristics under complex engineering constraints, which poses significant challenges theoretically and practically. This paper proposes an improved Dynamic programming (DP) algorithm to solve the EETC problem. This algorithm creates a state space table, layers the states according to the location of the road section, solves the objective function value of the state space table from the back to the front, and then obtains the optimized speed track. This algorithm optimizes the state space twice before and after offline computation, greatly reducing the number of state spaces and achieving memory storage of only about 400 MB (or even less). Based on this state storage, the optimized speed trajectory can be obtained within 20 ms. The proposed algorithm is compared with mixed integer Linear programming (MILP) and Convex optimization (CO). This method's real-time energy-saving optimization performance is similar to that of MILP and CO, and the real-time track acquisition speed is at the millisecond level. Moreover, it has no requirements for the high performance of the computer CPU and the allocation of high-quality stable solvers and has more advantages in security and practicality.