Abstract:
Leukemia is a type of cancer that affects the white blood cells in the bone
marrow. The basic cause of this disease is the inability of the bone marrow to produce healthy cells. Instead, abnormal white blood cells are being
produced that are called leukocytes. The rate of production of these leukocytes is very high and eventually they leave the bone marrow and spill into
the circulatory system. Chemotherapy is the most common treatment for
Leukemia. It naturally kills the rapidly growing cells in the human body so
normal or healthy cells are also killed along with leukemic or cancer cells. A
mathematical model of Acute Leukemia is considered in this research. The
effect of chemotherapeutic drug on normal and leukemic cells is represented
by a therapy function that are of two types namely monotonic therapy and
non-monotonic therapy. The monotonic therapy represents a direct relation ship with the therapeutic drug whereas non-monotonic therapy represents a
relationship which increases in the beginning and reaches a maximum level
at a point and then decreases after that point. The main objective of the
thesis is to design a controller for the therapeutic agent in order to minimize
the leukemic cells, maintain a safe amount of normal cells and ensure minimum amount of drug during the therapy process. Three nonlinear controllers
have been designed for this purpose; 1) Backstepping Controller 2) Integral
Backstepping Controller 3) Synergetic Controller. The nonlinear controllers
use Lyapunov based stability theory to analyze the system’s asymptotic sta bility and convergence of the leukemic cells to their desired reference. The
simulations have been performed in Matlab/Simulink and the results show
that both the therapies are effective enough to reduce the leukemic cells to
zero while a safe amount of normal cells has been retained using minimum
amount of therapeutic agent.
