A model for cancer chemotherapy with state-space constraints

Abstract

The analysis of optimal control problems is significantly more difficult when state space constraints are imposed and thus in many modelling approaches explicit constraints are handled by including penalty terms in the objective. In this paper, we use the example of a simple model for cancer chemotherapy to compare the structure of extremals when upper limits on the total number of cancer cells are imposed (a) implicitly through a penalty term in the objective and (b) explicitly in the form of state-space constraints.