Dynamic Programming Application for Pseudospectral Optimal Train Control Problem

This paper is focussed to solve the optimal train control problem using Pseudospectral method and application of Dynamic Programming. The primary objective in Energy-Efficient Train Control is to generate optimum speed profile under the given speed and gradient constraints so that the train reaches the destination within the allotted time. In this proposed methodology, the state and control variables are approximated using a global polynomial and collocation is performed at Legendre-Gauss-Lobatto points. Further, the transformed problem is solved using Dynamic Programming. The advantage of obtaining global optimum with Dynamic Programming is combined with possibility of reducing the calculation time by employing the Pseudospectral method is investigated. The choice of number of collocation points and its effect on the quality of optimum speed trajectory and computation times are provided in the simulation results. It is observed that the proposed method converges faster when compared with compared to Dynamic Programming performed in time domain.