Barrier function and terminal synergetic based controllers for the chemotherapy of brain tumor

Lumps formed by abnormal cell growth in the brain constitute brain tumors. Treatments differ depending on the specificity of the tumor and the condition of the patient; surgery, radiation therapy and targeted therapy are suggested for less severe tumors, while for severe tumors; chemotherapy is recommended. The last one, while being suggested and effective also in conjunction with surgery, has side effects that could be fatal. Therefore, it is mandatory to determine the appropriate dosage to obtain the desired effects without affecting healthy and immune cells. In this research work, advanced barrier function-based sliding mode and terminal synergetic-based controllers are designed to determine the amount of chemotherapy to eliminate tumor cells and maintain the right amount of healthy and immune cells. In particular, a barrier-based sliding mode controller is designed for dynamically controlling the chemotherapy drug for the tumor system, whereas the stability and convergence of the system are checked using the Lyapunov theory. The performance of the controller has been verified using MATLAB software based on different control parameters. The controller has remained successful in reducing the tumor cells and maintaining safe number of healthy and immune cells, showing favorable results in terms of steady-state error, over-under shoots, and rate of convergence.