The Train Control Problem
In 1977–78 Milroy  considered the problem of driving a train from one station to the next along a level track within a given allowable time in such a way that energy consumption is minimised. He used the energy flows in the traction and braking systems of the train to derive state variable equations with time as the independent variable and position and speed as the dependent state variables. He used an heuristic application of the Pontryagin Principle to conclude that the optimal driving strategy consisted of a maximum acceleration-coast-brake control sequence. Subsequent studies confirmed the optimality of this control sequence for short journeys, and showed that a speed-hold phase should be included on longer journeys.
KeywordsSpeed Profile Train Control Driving Advice Level Track Pontryagin Principle
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