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An optimal strategy for the control of a train

Published online by Cambridge University Press:  17 February 2009

Phil Howlett
Phil Howlett
Affiliation:
School of Mathematics and computer Studies, South Australian Institute of Technology, The Levels Campus, South Australia.
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Abstract

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A train travels from one station to the next along a level track. The journey must be completed within a given time and it is desirable to minimise the energy required to drive the train. It has been shown with an appropriate formulation of the problem that an optimal strategy exists and that this strategy must satisfy a Pontryagin type criterion. In this paper the Pontryagin principle will be used to find the nature of the optimal strategy and this information will then be used to determine the precise optimal strategy.

Type
Research Article
Information
The ANZIAM Journal , Volume 31 , Issue 4 , April 1990 , pp. 454 - 471
Copyright
Copyright © Australian Mathematical Society 1990

References

[1] Craven, B. D., Mathematical programming and control theory (Chapman and Hall, 1978).CrossRefGoogle Scholar
[2] Howlett, Phil, “Existence of an optimal strategy for the control of a train”, South Australian Institute of Technology, School of Mathematics Report (1987).Google Scholar
[3] Howlett, Phil, “Necessary conditions on an optimal strategy for the control of a train”, South Australian Institute of Technology, School of Mathematics Report (1987).Google Scholar
[4] Kautsky, J., Long, A. M., and Milroy, I. P., “Energy Conservation of Rail Vehicles”, Report to the Institution of Engineers, Australia (1983).Google Scholar
[5] Luenberger, D. G., Optimization by vector space methods (Wiley, 1969).Google Scholar
[6] Milroy, I. P., “Aspects of automatic train control”, Loughborough University Ph.D. Thesis, 1980.Google Scholar
[7] Tyler, K., “Energy minimization of rail vehicles”, South Australian Institute of Technology, Master of Applied Science Thesis, 1982.Google Scholar
[8] Yosida, K., Functional analysis (5th ed.Springer, 1978).CrossRefGoogle Scholar