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A Common Regularization for Three Reservoir Optimal Control Problems

Author

Listed:
  • H. X. Phu

    (Vietnam Academy of Science and Technology)

  • H. G. Bock

    (University of Heidelberg)

Abstract

Four optimal control problems of reservoir release are investigated. The first problem is to minimize the peak release in order to prevent flood and to reduce the flood height. The second problem is to maximize the lowest release in order to ensure irrigation, water supply, shipping and environment downstream. The third problem is to minimize the flooding duration in order to reduce damage to goods, possessions, plants, levees, etc. It is shown that these three problems may possess infinitely many different optimal solutions, but they all have a common optimal solution, which is the unique optimal solution of the fourth problem. Since this unique optimal solution depends continuously on the input data, the fourth problem is well-posed and it can be considered as a common regularization of the three ill-posed problems.

Suggested Citation

  • H. X. Phu & H. G. Bock, 2013. "A Common Regularization for Three Reservoir Optimal Control Problems," Journal of Optimization Theory and Applications, Springer, vol. 157(1), pages 199-228, April.
    • Handle: RePEc:spr:joptap:v:157:y:2013:i:1:d:10.1007_s10957-012-0173-8
    DOI: 10.1007/s10957-012-0173-8
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    References listed on IDEAS

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    1. N.C.P. Edirisinghe & E.I. Patterson & N. Saadouli, 2000. "Capacity Planning Model for a Multipurpose Water Reservoir with Target-Priority Operation," Annals of Operations Research, Springer, vol. 100(1), pages 273-303, December.
    2. Chatterjee, Bishu & Howitt, Richard E. & Sexton, Richard J., 1998. "The Optimal Joint Provision of Water for Irrigation and Hydropower," Journal of Environmental Economics and Management, Elsevier, vol. 36(3), pages 295-313, November.
    3. N. Umamahesh & P. Sreenivasulu, 1997. "Technical Communication: Two-Phase Stochastic Dynamic Programming Model for Optimal Operation of Irrigation Reservoir," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 11(5), pages 395-406, October.
    4. S. Arunkumar & K. Chon, 1978. "On Optimal Regulation Policies for Certain Multi-Reservoir Systems," Operations Research, INFORMS, vol. 26(4), pages 551-562, August.
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