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Optimal control of finite dams: continuous output procedure

Published online by Cambridge University Press:  01 July 2016

M. J. Faddy
M. J. Faddy*
Affiliation:
University of Birmingham
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Abstract

The problem discussed is that of controlling optimally the release of water from a finite dam, when the release rate may vary continuously and the optimality is defined in terms of a cost structure imposed on the operation of the dam. A diffusion model is suggested and by considering a family of plausible output policies, the control problem is reduced to the solution of a free boundary problem associated with a certain partial differential equation. A set of necessary conditions for the optimal choice of these boundaries is established and a method of solution is suggested. By using this method, together with well-established computational techniques, numerical solutions are obtained. These numerical solutions indicate that this optimal policy does not result in very much improvement over a much simpler policy where the output rate is constrained to take only two values.

Keywords

DAMSCONTROLDIFFUSION MODELPOTENTIAL COST FUNCTIONOPTIMAL PROCEDURES
Type
Research Article
Information
Advances in Applied Probability , Volume 6 , Issue 4 , December 1974 , pp. 689 - 710
Copyright
Copyright © Applied Probability Trust 1974 

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References

[1] Bather, J. A. (1963) Control charts and the minimisation of costs. J. R. Statist. Soc. B 25, 49–80.Google Scholar
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[3] Burkill, J. C. (1962) The Theory of Ordinary Differential Equations. Oliver and Boyd, Edinburgh.Google Scholar
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[5] Faddy, M. J. (1974) Optimal control of finite dams: discrete (2-stage) output procedure. J. Appl. Prob. 11, 111–121.CrossRefGoogle Scholar
[6] Hamming, R. W. (1962) Numerical Methods for Scientists and Engineers. McGraw-Hill, New York.Google Scholar