Optimal sliding mode control of drug delivery in cancerous tumour chemotherapy considering the obesity effects

Abstract

Different control strategies have been proposed for drug delivery in chemotherapy during recent years. These control algorithms are designed based on dynamic models of various orders. The order of the model depends on the number of effects considered in the model. In a recent model, the effect of obesity on the tumour progression and optimal control strategy in chemotherapy have been investigated in a fifth-order state-space model. However, the optimal controller is open loop and not robust to the common uncertainties of such biological system. Here, the sliding surface is obtained by the optimal trajectory and by considering uncertainties of some parameters, the robust-sliding control law is formulated in a way to slid on the optimal surface. Then, a sliding mode controller is designed to determine the drug dose rate such that the system follows the optimal desired trajectory. The stability of the control system is proved and the simulation results indicate that three states track the trajectory and the remaining two states satisfy the constraints.