Piecewise constant suboptimal controls for a system describing tumor growth under angiogenic treatment

A mathematical model for tumor anti-angiogenesis formulated by Ergun et al. [9] is considered as an optimal control problem with the aim of maximizing the tumor reduction achievable with an a priori given amount of anti-angiogenic agents. Optimal controls contain a segment along which the dosage follows a time-varying feedback control. With current medical technologies such a design is not realistic. In this paper the efficiency of piecewise constant, open-loop protocols with a small number of switchings is compared with the theoretically optimal solution derived earlier. It is shown that these protocols generally provide excellent suboptimal strategies, even when the times of applications are restricted to follow daily patterns.