Lyapunov based nonlinear controllers for the chemotherapy of brain tumor

Among various methods for the treatment of brain tumor include surgery, chemotherapy, radiation therapy etc. For less severe tumors, i.e. benign, applying surgery is suitable because they are small in size and have definite edges. While in case of severe tumors, i.e. malignant chemotherapy is preferable: suggesting surgery is not always a good option as these tumors do not have definite boundaries and are attached very closely with sensitive tissues of brain. In this research work three nonlinear controllers: (1) Lyapunov redesign, (2) sliding mode, (3) terminal sliding mode based controllers have been designed for the therapeutic agent in an updated model of brain tumor in order to minimize the number of brain tumor cells, to maintain a safe amount of healthy cells, to keep immune cells above a certain value and ensure the use of suitable amount of drug for the therapy. Lyapunov stability theory has been used to analyze the system's asymptotic stability and convergence of the tumor cells to their desired reference. Simulations have been performed in ODE45-Solver using Matlab/Simulink and the results show that chemotherapy is effective enough to get the desired objectives.