Bang-bang optimal control for the dam problem |
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Authors: | Avner Friedman Shaoyun Huang Jiongmin Yong |
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Affiliation: | (1) Mathematics Department, Purdue University, 47907 West Lafayette, IN, USA;(2) Peking University, Peking, People's Republic of China |
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Abstract: | The dam problem with general geometry is considered. Fluid is drawn from the bottomS1 at a ratek where 0 k N, S1k M; the objective is to minimize the total pressure of the fluid in the dam. A bang-bang principle is established for any optimal controlk0, that is,k0 = 0 on a setA andk0 =N on the complement setS1A. In the case of a rectangular dam the structure ofA is determined and the uniqueness of the minimizerk0 is established.This work is partially supported by National Science Foundation Grants DMS-8501397 and DMS-8420896. |
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