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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.

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.

infinite horizon optimal control, existence theorem, weighted Sobolev spaces, model of cancer treatment, numerical solution.

http://dx.doi.org/10.1080/00207179.2017.1396362