# The Optimal Control of a Train

*Phil Howlett* ()

*Annals of Operations Research*, 2000, vol. 98, issue 1, 65-87

**Abstract:**
We consider the problem of determining an optimal driving strategy in a train control problem with a generalised equation of motion. We assume that the journey must be completed within a given time and seek a strategy that minimises fuel consumption. On the one hand we consider the case where continuous control can be used and on the other hand we consider the case where only discrete control is available. We pay particular attention to a unified development of the two cases. For the continuous control problem we use the Pontryagin principle to find necessary conditions on an optimal strategy and show that these conditions yield key equations that determine the optimal switching points. In the discrete control problem, which is the typical situation with diesel-electric locomotives, we show that for each fixed control sequence the cost of fuel can be minimised by finding the optimal switching times. The corresponding strategies are called strategies of optimal type and in this case we use the Kuhn–Tucker equations to find key equations that determine the optimal switching times. We note that the strategies of optimal type can be used to approximate as closely as we please the optimal strategy obtained using continuous control and we present two new derivations of the key equations. We illustrate our general remarks by reference to a typical train control problem. Copyright Kluwer Academic Publishers 2000

**Keywords:** train control; optimal control; discrete control; optimal switching times (search for similar items in EconPapers)

**Date:** 2000

**References:** Add references at CitEc

**Citations:** View citations in EconPapers (26) Track citations by RSS feed

**Downloads:** (external link)

http://hdl.handle.net/10.1023/A:1019235819716 (text/html)

Access to full text is restricted to subscribers.

**Related works:**

This item may be available elsewhere in EconPapers: Search for items with the same title.

**Export reference:** BibTeX
RIS (EndNote, ProCite, RefMan)
HTML/Text

**Persistent link:** https://EconPapers.repec.org/RePEc:spr:annopr:v:98:y:2000:i:1:p:65-87:10.1023/a:1019235819716

**Ordering information:** This journal article can be ordered from

http://www.springer.com/journal/10479

**DOI:** 10.1023/A:1019235819716

Access Statistics for this article

Annals of Operations Research is currently edited by *Endre Boros*

More articles in Annals of Operations Research from Springer

Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().