Seyed Mohammad Hashemi - Department of Electrical Engineering South Tehran Branch, Islamic Azad University Tehran, Iran
Amir Hooshang Mazinan - Department of Electrical Engineering South Tehran Branch, Islamic Azad University Tehran, Iran
Mohammad Bagher Menkaj - Department of Electrical Engineering Amirkabir University of Technology Tehran, Iran

The detrimental effects of chemotherapy to fight the cancer cells and drug-resistant in the body are to the extent that they can be even more lethal than cancer if not concerned. Therefore, this study aims to provide a short-time solution for the cancer treatment. In this paper, a comprehensive mathematical model of cancer treatment including radiotherapy, chemotherapy, and metastasis is presented. An in-depth investigation of the mentioned model reveals the unstability of the system around the equilibrium point. Hence, in order to stabilize the system around the equilibrium point, a solution considering the detrimental effects caused by chemotherapy should be provided. The sliding mode control in which the sliding surface is extracted by using the optimal control theory can well meet the above objectives. The suggested optimal sliding mode control, in addition to flexibility in designing the control protocol of non-linear models, is highly resistant against the uncertainties of the presented mathematical cancer model. Finally, the proposed protocol is investigated for two patients. The effectiveness of the proposed technique regarding a short-time full treatment and removing the need for receiving drugs at the end of period is well established.

cancer; tumor growth mathematical modeling; sliding mode control; optimal sliding surface