Hostname: page-component-cd9895bd7-p9bg8 Total loading time: 0 Render date: 2024-12-23T16:45:10.540Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Get access Rights & Permissions [Opens in a new window]

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 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

[1] Bather, J. A. (1963) Control charts and the minimisation of costs. J. R. Statist. Soc. B 25, 49–80.Google Scholar
[2] Bather, J. A. (1968) A diffusion model for the control of a dam. J. Appl. Prob. 5, 55–71.Google Scholar
[3] Burkill, J. C. (1962) The Theory of Ordinary Differential Equations. Oliver and Boyd, Edinburgh.Google Scholar
[4] Doob, J. L. (1953) Stochastic Processes. John Wiley, New York.Google Scholar
[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