Robust Control for Cancer Chemotherapy Through Time Delayed Estimation Philosophy

Abstract

Chemotherapy, a vital cancer treatment, operates by delivering drugs to target and eliminate cancer cells in the patient body. Mathematical models like the log-kill, Norton-Simon, and $E_{\max }$ hypotheses describe the growth/shrinking of the cancerous tumor due to the interaction and administration of the drugs with the tumor. This paper proposes a robust control approach based on artificial time-delayed theory to track the desired rate of change in tumor volume under model uncertainties and disturbances. The proposed algorithm relaxes the assumption on a priori knowledge of disturbance bound and its derivative. Unlike traditional methods, the control structure is simple, and the total disturbance is estimated by analyzing the previous input and output of the feedback state and control variables. Thus, robustness is ensured without relying on high-frequency switching or high gain. The stability analysis of the proposed scheme is investigated based on the Lyapunov theory. Moreover, extensive simulation results with comparative analysis affirm the efficacy of the proposed approach.

Keywords

• Cancer chemotherapy
• cell-kill hypotheses
• robust control
• trajectory tracking
• time-delayed control