State-constrained optimal control applied to cell-cycle-specific cancer chemotherapy

In this paper, the optimal drug injection problem arising in cancer treatment by cell-cycle-specific chemotherapy is investigated. The optimal control problem is state constrained in which the stage cost reflects the concern of maximal drug injection, while the state constraint imposes a lower bound on the total number of cells in the bone marrow. It is shown that this problem can be approximately solved up to any desired precision by using an indexed family of state-unconstrained optimal control problems. The state constraint is fulfilled for any member of the family. The existence of solutions is proved and the resulting approximation is characterized by appropriate two-sided inequalities. Simulations are provided to show the efficiency and relevance of the proposed formulation.