Adaptive terminal and supertwisting sliding mode controllers for acute Leukemia therapy

The form of cancer related to the abnormal growth and division of leukocytes in the blood is called Leukemia whose most common method of treatment is chemotherapy which has a disadvantage of killing normal cells along with cancer cells. Monotonic and non-monotonic therapy functions have been used in the manuscript to describe different effects of treatment on both the normal and the leukemic cells by utilizing model of acute leukemia. Michaelis-Menten equation describes the behavior of monotonic function whereas the function with a threshold impact is known as non-monotonic function. Adaptive terminal sliding mode controller (AT-SMC) with input saturation, super-twisting sliding mode controller (ST-SMC) and synergetic controller have been proposed in this paper to attain the objectives of killing the leukemic cells and maintain a safe number of normal cells by using a safe value of total chemotherapeutic agent. Lyapunov stability theory has been used to analyze the stability of the designed controllers and Matlab/Simulink has been used to simulate them and their performance has been analyzed on the basis of transient response characteristics, steady state accuracy and robustness.