The aim of this paper is to investigate the optimal control problem for finite-dimensional bilinear systems and its application to a chemotherapy model. We characterize an optimal control that minimizes a quadratic cost functional in two cases of constrained admissible controls, then we give sufficient conditions for the uniqueness of such a control, and we derive useful algorithms for the computation of the optimal control. The established results are applied to a cancer chemotherapy bilinear model in order to simulate the optimal treatment protocol using two different approaches: one based on a limited instant toxicity, and the other on a limited cumulative toxicity along the therapy session.
