Management of a large dam via optimal price control

Boris Miller, Daniel McInnes

Research output: Chapter in Book/Report/Conference proceedingConference PaperResearchpeer-review

5 Citations (Scopus)

Abstract

This paper considers the optimal management of a dam with its level approximated by N discrete states and modeled via a continuous-time controlled Markov chain on a finite time horizon. The inflow process is seasonal, and so non-stationary, as are the customer demands. The control takes the form of price, the bounds of which are set by regulators, and we take into account the individual sectoral demands of customers. The general approach to the solution of this problem is to consider the stochastic optimization problem in the average sense and solve it via dynamic programming. We show that an optimal price can be obtained for each state based on minimizing the difference between desired and optimal consumption, and minimizing the probability that the dam level falls below a prescribed level both on the control period and at the terminal time. The result is illustrated by a numerical example.
Original languageEnglish
Title of host publicationProceedings of the 18th World Congress: The International Federation of Automatic Control
EditorsSergio Bittanti, Angelo Cenedese, Sandro Zampieri
Place of PublicationMilan Italy
PublisherInternational Federation of Automatic Control
Pages12432 - 12438
Number of pages7
Volume18
DOIs
Publication statusPublished - 2011
EventInternational Federation of Automatic Control World Congress 2011 - Università Cattolica del Sacro Cuore, Milano, Italy
Duration: 28 Aug 20112 Sep 2011
Conference number: 18th
https://www.ifac2011.org/

Conference

ConferenceInternational Federation of Automatic Control World Congress 2011
Abbreviated titleIFAC 2011
CountryItaly
CityMilano
Period28/08/112/09/11
Internet address

Cite this

Miller, B., & McInnes, D. (2011). Management of a large dam via optimal price control. In S. Bittanti, A. Cenedese, & S. Zampieri (Eds.), Proceedings of the 18th World Congress: The International Federation of Automatic Control (Vol. 18, pp. 12432 - 12438). Milan Italy: International Federation of Automatic Control. https://doi.org/10.3182/20110828-6-IT-1002.00786
Miller, Boris ; McInnes, Daniel. / Management of a large dam via optimal price control. Proceedings of the 18th World Congress: The International Federation of Automatic Control. editor / Sergio Bittanti ; Angelo Cenedese ; Sandro Zampieri. Vol. 18 Milan Italy : International Federation of Automatic Control, 2011. pp. 12432 - 12438
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Miller, B & McInnes, D 2011, Management of a large dam via optimal price control. in S Bittanti, A Cenedese & S Zampieri (eds), Proceedings of the 18th World Congress: The International Federation of Automatic Control. vol. 18, International Federation of Automatic Control, Milan Italy, pp. 12432 - 12438, International Federation of Automatic Control World Congress 2011, Milano, Italy, 28/08/11. https://doi.org/10.3182/20110828-6-IT-1002.00786

Management of a large dam via optimal price control. / Miller, Boris; McInnes, Daniel.

Proceedings of the 18th World Congress: The International Federation of Automatic Control. ed. / Sergio Bittanti; Angelo Cenedese; Sandro Zampieri. Vol. 18 Milan Italy : International Federation of Automatic Control, 2011. p. 12432 - 12438.

Research output: Chapter in Book/Report/Conference proceedingConference PaperResearchpeer-review

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Miller B, McInnes D. Management of a large dam via optimal price control. In Bittanti S, Cenedese A, Zampieri S, editors, Proceedings of the 18th World Congress: The International Federation of Automatic Control. Vol. 18. Milan Italy: International Federation of Automatic Control. 2011. p. 12432 - 12438 https://doi.org/10.3182/20110828-6-IT-1002.00786