@misc{LykinaGrass, author = {Lykina, Valeriya and Grass, Dieter}, title = {Infinite horizon cancer treatment model with isoperimetrical constraint: existence of optimal solutions and numerical analysis}, series = {International Journal of Control}, volume = {92}, journal = {International Journal of Control}, number = {6}, issn = {1366-5820}, doi = {10.1080/00207179.2017.1396362}, pages = {1401 -- 1414}, 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 OCMat, which implements a continuation method for solving discounted infinite horizon optimal control problems.}, language = {en} }