Double Integral sliding mode control of Leukemia Therapy

Abstract

Leukemia is a form of cancer caused by the presence of large number of leukocytes in the blood and bone marrow and is commonly known as cancer of blood and bone marrow. This form of cancer is responsible for the rapid production of abnormal white blood cells in the circulatory system. Chemotherapy is the most common treatment of cancer and generally kills the Leukemic as well as some normal cells. Three nonlinear controllers namely Sliding Mode Controller (SMC), Integral Sliding Mode Controller (ISMC) and Double Integral Sliding Mode Controller (DISMC) have been designed using the model of Acute Leukemia under the effect of Chemotherapy treatment. The effect of therapy on normal and Leukemic cells has been described by two therapy functions namely monotonic and non-monotonic therapy function. Monotonic therapy function is based on Michaelis–Menten equation in which the effect of therapy depends on the amount of therapeutic agent used whereas the non-monotonic therapy function has a threshold effect in which the effect of drug reaches maximum value at some point and then decreases after that point. The main objective of this research is to track the Leukemic cells to zero, track and retain normal cells to a safe number and ensure minimum safe application of total quantity of therapeutic agent during the therapy process. The system has been analyzed using Lyapunov based stability theory. The controllers have been simulated using Matlab/Simulink and their performance has been compared with each other on the basis of convergence of all states to their desired references and steady state accuracy.