Publications in Scientific Journals:
D. Grass, V. Lykina:
"Infinite horizon cancer treatment model with isoperimetrical constraint: existence of optimal solutions and numerical analysis";
International Journal of Control,
(2017),
29 pages.
English abstract:
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 OCMat2, which implements a continuation method for solving discounted infinite horizon optimal control problems.
Keywords:
infinite horizon optimal control, existence theorem, weighted Sobolev spaces, model of cancer treatment, numerical solution.
"Official" electronic version of the publication (accessed through its Digital Object Identifier - DOI)
http://dx.doi.org/10.1080/00207179.2017.1396362
Created from the Publication Database of the Vienna University of Technology.