Adaptive Tracking Control for Uncertain Cancer-Tumor-Immune Systems

In this paper, the problem of control is investigated for cancer-tumor-immune systems, based on a two-dimension uncertain nonlinear model describing the interaction between immune and cancer cells in a body. First, the control problem is transformed into a state tracking problem. Second, an adaptive control method is proposed to track and stop the growth of cancer and maintain cancer and immune cells at an acceptable level. Different from the existing results in literature, the singularity problem in controller and the inaccuracy in control design have been overcome. From theoretical analysis, it is shown that the resulting closed-loop system is asymptotically stable and the tracking errors converge to the origin. Finally, simulation results illustrate not only the competitive relationship between immune system and tumor, but also the immune system has strong immunity to low level tumor volumes.