Small penalty control of the end temperature in a long rod

A. K. Gautesen*, W. E. Olmstead

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

1 Scopus citations


The problem considered is that of maintaining the end temperature of a long rod near a prescribed level over a fixed time interval. Control is achieved via the heat flux at the near end, and it is optimal in the sense that it minimizes a given performance index of quadratic form. The performance index contains a penalty parameter associated with the magnitude of the control. Particular attention is given to the determination of the optimal control when the penalty parameter is small (i.e., cheap control). This gives rise to a singularly perturbed integral equation, which is solved asymptotically by a methodology which has recently been developed for a related class of problems.

Original languageEnglish (US)
Pages (from-to)443-454
Number of pages12
JournalJournal of Optimization Theory and Applications
Issue number3
StatePublished - Sep 1 1990


  • Optimal control
  • heat transfer
  • singularly perturbed integral equations

ASJC Scopus subject areas

  • Control and Optimization
  • Management Science and Operations Research
  • Applied Mathematics


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