Oncolytic virotherapy with measles represents a promising approach to combat cancer, often combined with other therapies to eradicate tumors. However, it faces many challenges, for instance, the toxic side effects that must be carefully managed during treatment, the optimal dose to apply, the determination time to extirpate the tumor, the monitoring system, and others. In this study, predictive control methodologies are employed based on the nonlinear system representing oncolytic virotherapy with measles. The objective is to present strategies for cancer treatment by either limiting the maximum dose per patient or bringing the tumor to a point where it can be surgically removed. This method utilizes system approximations at discrete time intervals for the model subsystems. To address the limitation of the maximum allowed injected virus dose, an additional state describing the total injected dose is incorporated. Simulations demonstrate dose optimization for tumor reduction, with successful therapy in up to 18 days. Moreover, careful dosing strategies maximize therapeutic efficacy while minimizing potential toxicity, underscoring the promising potential in achieving optimal treatment outcomes. These findings support the idea that feedback control has the potential to enhance robustness and toxicity reduction in oncolytic virotherapy.