Optimal driving strategies for a train journey with non-zero track gradient and speed limits

Abstract

In this paper we formulate and solve an important problem in applied optimal control. A train is to be driven along a track with non-zero gradient, where speed limits are imposed. The journey is to be completed within a specified time using as little fuel as possible. We find key equations that determine strategies of optimal type and present a general solution algorithm. Several specific examples will be given to illustrate the solution procedure.