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.
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This research was funded by Vietnam National Foundation for Science and Technology Development under grant number 101.02-2011.45. The authors thank the editors and the referees for their helpful comments.
Communicated by Nguyen Dong Yen.
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Phu, H.X., Bock, H.G. A Common Regularization for Three Reservoir Optimal Control Problems. J Optim Theory Appl 157, 199–228 (2013). https://doi.org/10.1007/s10957-012-0173-8
- Optimal control
- Reservoir release
- Flood prevention
- Flood damage reduction
- Water supply