A Restricted Variation Argument to Derive Necessary Conditions for the Optimal Control of a Train

Howlett, Phil

doi:10.1007/978-1-4613-0301-5_20

Phil Howlett⁴

Part of the book series: Applied Optimization ((APOP,volume 39))

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Abstract

A train travels from one station to the next along a smooth track with known gradient. The journey must be completed within a given time and it is desirable to minimise fuel consumption. We assume that only certain discrete control settings are possible. This conforms to the most common situation in diesel-electric locomotives. In the case where the track is flat and the train is controlled using a finite sequence of traction controls and a final brake control Cheng and Howlett (1992) have derived necessary and sufficient conditions that define the optimal switching times. In this paper we will show that these conditions can be derived (as necessary conditions) using an elegant argument of restricted variation.

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Centre for Indutrial and Applicable Mathematics, The University of South Australia, The Levels, South Australia, Australia
Phil Howlett

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Editors and Affiliations

Department of Applied Mathematics, The Hong Kong Polytechnic University, Kowloon, Hong Kong, China
Xiaoqi Yang Ph. D. (Assistant Professor) (Assistant Professor)
The University of Western Australia, Perth, Australia
Les Jennings

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Howlett, P. (2000). A Restricted Variation Argument to Derive Necessary Conditions for the Optimal Control of a Train. In: Yang, X., Mees, A.I., Fisher, M., Jennings, L. (eds) Progress in Optimization. Applied Optimization, vol 39. Springer, Boston, MA. https://doi.org/10.1007/978-1-4613-0301-5_20

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DOI: https://doi.org/10.1007/978-1-4613-0301-5_20
Publisher Name: Springer, Boston, MA
Print ISBN: 978-1-4613-7986-7
Online ISBN: 978-1-4613-0301-5
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