Optimal control for a bilinear model with recruiting agent in cancer chemotherapy

We consider a general mathematical model for cancer chemotherapy as optimal control problem for a bilinear system and give necessary and sufficient conditions for strong local optimality of bang-bang controls. These results apply to a 3-compartment model, which besides a killing agent also includes a recruiting agent, i.e. a drug which acts on the residuum of dormant cells in the cell cycle. For this model it is shown that singular controls are not optimal, in fact singular regimes for the killing agent are locally maximizing with many extremal bang-bang trajectories near the non-optimal singular arc. Our results allow to distinguish between locally optimal and non-optimal bang-bang controls.