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Optimal control of a heat conduction problem

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Summary

This paper treats the problem of optimal control of a class of linear distributed parameter systems. Fourier series are used for transformation of a one-dimensional heat conduction equation into a system of ordinary differential equations. Necessary conditions for the optimal control are derived by means of Pontryagin's maximum principle. The application of obtained results is shown through two examples. The method in this paper is limited to linear systems.

Zusammenfassung

Die Arbeit befaßt sich mit dem Problem der optimalen Steuerung einer Klasse von Systemen deren mathematisches Modell durch partielle Differentialgleichungen gegeben wird. Fourier'sche Reihen werden benutzt, um die eindimensionale Wärmeleitungsgleichung in das System gewöhnlicher Differentialgleichungen zu transformieren. Die Bedingungen zur optimalen Steuerung wurden unter Benutzung des Maximumprinzips von Pontrjagin abgeleitet. Die Anwendung der gewonnenen Ergebnisse wird mit Hilfe zweier Beispiele dargestellt. Die Methode, die in der Arbeit dargelegt wird, ist auf lineare Systeme begrenzt.

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Authors and Affiliations

  1. Mechanical Engineering Faculty, University of Novi Sad, Yugoslavia

    Dusan P. Petrovački

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  1. Dusan P. Petrovački
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Petrovački, D.P. Optimal control of a heat conduction problem. Journal of Applied Mathematics and Physics (ZAMP) 26, 463–480 (1975). https://doi.org/10.1007/BF01590783

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  • DOI: https://doi.org/10.1007/BF01590783

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