Optimal control of single retention reservoir during flood: Solution of deterministic, continuous-time problems
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In this paper, a theoretical analysis of the problem of water reservoir control during flood is presented. The control goal considered is the reduction of the damages caused by high level of water in a flood plain below the reservoir. It is assumed that these damages depend on the culminant release from the reservoir. The paper contains the derivation of the necessary conditions of optimality (in the form of a maximum principle) as well as the analysis of solutions for various (general) deterministic inflow scenarios, while taking into account the complete description of the reservoir constraints.
Key WordsFlood control minimax problems state constraints mixed control-state constraints weak maximum principle
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- 1.Pytlak, R., andMalinowski, K.,Optimal Scheduling of Reservoir Releases During Flood: Deterministic Optimization Problem, Parts 1 and 2, Journal of Optimization Theory and Applications, Vol. 61, No. 3, pp. 409–432, 1989 and Vol. 61, No. 3, pp. 433–449, 1989.Google Scholar
- 2.Windsor, J. S.,Optimization Models for the Operation of Flood Control Systems, Water Resources Research, Vol. 9, No. 5, pp. 1219–1226, 1973.Google Scholar
- 3.Karbowski, A.,Synthesis of Structures and Mechanisms of Flood Control in Multireservoir Systems, Warsaw University of Technology, PhD Thesis, 1989 (in Polish).Google Scholar
- 4.Malinowski, K., andKarbowski, A.,Hierarchical Structure with Repetitive Goal Coordination for Real-Time Flood Control in a Multireservoir System, Proceedings of the IFAC Conference on Systems Analysis Applied to Water and Related Land Resources, Pergamon Press, Oxford, England, 1986.Google Scholar
- 5.Malinowski, K., Karbowski, A., andSalewicz, K. A.,Hierarchical Control Structures for Real-Time Scheduling of Releases in a Multireservoir System during Flood, Proceedings of the IFAC/IFORS Symposium on Large-Scale Systems in Theory and Applications, Pergamon Press, Oxford, England, 1987.Google Scholar
- 6.Hughes, W. C.,Flood Control Release Optimization Using Methods from Calculus, Journal of the Hydraulic Division of the ASCE, Vol. 97, No. 5, pp. 691–704, 1971.Google Scholar
- 7.Dubovitskii, A. Y., andMilyutin, A. A.,Extremum Problems in the Presence of Constraints, Zhurnal Vychislitelnoi Matematiki i Matematicheskoi Fiziki, Vol. 5, No. 3, pp. 395–453, 1965 (in Russian).Google Scholar
- 8.Dubovitskii, A. Y., andMilyutin, A. A.,Necessary Conditions of Weak Extremum in Optimal Control Problems with Mixed Inequality Constraints, Zhurnal Vychislitelnoi Matematiki i Matematicheskoi Fiziki, Vol. 8, No. 4, pp. 725–779, 1968 (in Russian).Google Scholar
- 9.Neustadt, L. W.,Optimization: A Theory of Necessary Conditions, Princeton University Press, Princeton, New Jersey, 1976.Google Scholar
- 10.Kolmogorov, A. N., andFomin, S. V.,Elements of the Theory of Functions and Functional Analysis, Nauka, Moscow, USSR, 1978 (in Russian).Google Scholar
- 11.Stoer, J., andBulirsch, R.,Introduction to Numerical Analysis, Springer-Verlag, New York, New York, 1983.Google Scholar