Optimal control of the end-temperature in a semi-infinite rod

W. E. Olmstead; W. E. Schmitendorf

doi:10.1007/BF01601345

Optimal control of the end-temperature in a semi-infinite rod

W. E. Olmstead^*, W. E. Schmitendorf

^*Corresponding author for this work

Engineering Sciences and Applied Mathematics

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

Abstract

The temperature distribution in a semi-infinite rod is controlled by heat input at one end. The objective is to keep the temperature at this end of the rod close to a given value, without excessive heat input. This distributed parameter optimal control problem is reformulated as a calculus of variations problem for the optimal end-temperature. An explicit solution is derived, and its general properties are examined. Two example cases are provided to illustrate the results.

Original language	English (US)
Pages (from-to)	697-706
Number of pages	10
Journal	Zeitschrift für angewandte Mathematik und Physik ZAMP
Volume	28
Issue number	4
DOIs	https://doi.org/10.1007/BF01601345
State	Published - Jul 1 1977

ASJC Scopus subject areas

Mathematics(all)
Physics and Astronomy(all)
Applied Mathematics

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10.1007/BF01601345

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abstract = "The temperature distribution in a semi-infinite rod is controlled by heat input at one end. The objective is to keep the temperature at this end of the rod close to a given value, without excessive heat input. This distributed parameter optimal control problem is reformulated as a calculus of variations problem for the optimal end-temperature. An explicit solution is derived, and its general properties are examined. Two example cases are provided to illustrate the results.",

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AB - The temperature distribution in a semi-infinite rod is controlled by heat input at one end. The objective is to keep the temperature at this end of the rod close to a given value, without excessive heat input. This distributed parameter optimal control problem is reformulated as a calculus of variations problem for the optimal end-temperature. An explicit solution is derived, and its general properties are examined. Two example cases are provided to illustrate the results.

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Optimal control of the end-temperature in a semi-infinite rod

Abstract

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