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Bang-bang optimal control for the dam problem

Bang-bang optimal control for the dam problem The dam problem with general geometry is considered. Fluid is drawn from the bottomS 1 at a ratek where 0 ≤k ≤ N, ∫ S 1 k ≤ M; the objective is to minimize the “total pressure” of the fluid in the dam. A bang-bang principle is established for any optimal controlk 0, that is,k 0 = 0 on a setA andk 0 =N on the complement setS 1 ∖A. In the case of a rectangular dam the structure ofA is determined and the uniqueness of the minimizerk 0 is established. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Applied Mathematics and Optimization Springer Journals

Bang-bang optimal control for the dam problem

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References (11)

Publisher
Springer Journals
Copyright
Copyright © 1987 by Springer-Verlag New York Inc.
Subject
Mathematics; Calculus of Variations and Optimal Control; Optimization; Systems Theory, Control; Theoretical, Mathematical and Computational Physics; Mathematical Methods in Physics; Numerical and Computational Physics, Simulation
ISSN
0095-4616
eISSN
1432-0606
DOI
10.1007/BF01442646
Publisher site
See Article on Publisher Site

Abstract

The dam problem with general geometry is considered. Fluid is drawn from the bottomS 1 at a ratek where 0 ≤k ≤ N, ∫ S 1 k ≤ M; the objective is to minimize the “total pressure” of the fluid in the dam. A bang-bang principle is established for any optimal controlk 0, that is,k 0 = 0 on a setA andk 0 =N on the complement setS 1 ∖A. In the case of a rectangular dam the structure ofA is determined and the uniqueness of the minimizerk 0 is established.

Journal

Applied Mathematics and Optimization – Springer Journals

Published: Mar 23, 2005

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