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Infinite horizon cancer treatment model with isoperimetrical constraint: existence of optimal solutions and numerical analysis

  • In this paper, a class of infinite horizon optimal control problems with a mixed control-state isoperimetrical constraint, also interpreted as a budget constraint, is considered. The underlying dynamics is assumed to be affine-linear in control. The crucial idea which is followed in this paper is the choice of a weighted Sobolev space as the state space. For this class of problems, we establish an existence result and apply it to a bilinear model of optimal cancer treatment with an isoperimetrical constraint including the overall amount of drugs used during the whole therapy horizon. A numerical analysis of this model is provided by means of open source software package OCMat, which implements a continuation method for solving discounted infinite horizon optimal control problems.

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Metadaten
Author: Valeriya Lykina, Dieter Grass
DOI:https://doi.org/10.1080/00207179.2017.1396362
ISSN:1366-5820
ISSN:0020-7179
Title of the source (English):International Journal of Control
Document Type:Scientific journal article peer-reviewed
Language:English
Year of publication:2019
Tag:existence theorem; infinite horizon optimal control; numerical solution; weighted sobolev spaces
Volume/Year:92
Issue number:6
First Page:1401
Last Page:1414
Faculty/Chair:Fakultät 1 MINT - Mathematik, Informatik, Physik, Elektro- und Informationstechnik / FG Mathematik insbesondere Optimierung
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