State Dependent Riccati Equation based Model Reference Adaptive Control for Finite Duration Cancer Treatment by using a Mixed Therapy

Almost all cancer treatment protocols have two main drawbacks. The first is the relapse of the tumor growth after recessing the treatment and the second is knowing the system parameters in order to design the controller. Due to toxicity of drugs and drug resistance effect the duration of the treatment must be limited. In this paper, a modified mathematical model for tumor growth has been proposed which the effect of chemotherapy and vaccine therapy on the parameters of the system has been considered. The main objective of this paper is to propose optimal finite duration cancer treatment for a patient with unknown model’s parameters. Stability analysis by using experimental data shows that the tumor free equilibrium point is unstable. Hence, changing the dynamics of the system around this equilibrium point for achieving finite duration treatment is essential. Hence, a mixed chemo-vaccine therapy is proposed. The role of the vaccine therapy is reinforcement of the immune system of the body (by changing the parameters of the system) and the role of the chemotherapy is pushing the trajectory of the system inside the domain of attraction of this stabilized equilibrium point. For achieving this target the MRAC-SDRE method has been used.