Optimal robust control of drug delivery in cancer chemotherapy: A comparison between three control approaches

During the drug delivery process in chemotherapy, both of the cancer cells and normal healthy cells may be killed. In this paper, three mathematical cell-kill models including log-kill hypothesis, Norton-Simon hypothesis and Emax hypothesis are considered. Three control approaches including optimal linear regulation, nonlinear optimal control based on variation of extremals and H∞-robust control based on μ-synthesis are developed. An appropriate cost function is defined such that the amount of required drug is minimized while the tumor volume is reduced. For the first time, performance of the system is investigated and compared for three control strategies; applied on three nonlinear models of the process. In additions, their efficiency is compared in the presence of model parametric uncertainties. It is observed that in the presence of model uncertainties, controller designed based on variation of extremals is more efficient than the linear regulation controller. However, H∞-robust control is more efficient in improving robust performance of the uncertain models with faster tumor reduction and minimum drug usage.