On an optimal control problem of train operation

This paper examines the operation of a train on a variable grade profile subject to arbitrary speed restrictions. The purpose of the study is to determine a detailed program for traction and brake applications, which minimizes energy consumption in moving the train along a given route for a given time. Stated in the form of optimal control, this problem is solved by constructing a numerical algorithm which essentially exploits analytical properties of the optimal solution obtained from the maximum principle analysis. Due to its analytical origin, the algorithm has inherent accuracy and adequate quick-operation that are demonstrated in numerical examples.