Deriving a suitable schedule through robust H_∞ and sliding mode control methods for cancer treatment using...

For malignant or blood-related cancers associated with the angiogenesis process, one of the most effective treatments is chemotherapy. To control the angiogenesis, anti-angiogenic drugs are typically used. In this research, we use a realistic nonlinear dynamic model representing the concentrations of normal cells, cancer cells, endothelial cells, chemotherapy agent and anti-angiogenic agent. Two algorithms including the sliding mode control and robust H_∞ control based on μ-synthesis are proposed to cure the cancer. Determined drugs' schedules by the controllers are implemented in both continuous and discrete time manners. According to the results, both control plans demonstrate a satisfying performance in the presence of parametric uncertainties, for the time step of one day which is the time step of continuous system. For the sliding mode control, time steps up to seven days has a good performance for nonlinear system but the robust H_∞ control for time steps of more than one day is unstable. For time step of one day, in the presence of parametric uncertainties, the closed loop system's trajectories move toward curative state and concentration of cancer cells tend to zero amount after a limited interval time of treatment. This means that based on the proposed drugs' scheduling, the chemotherapy agent effectively targets and kills the cancer cells.