Optimal Control of Immunogenic Tumor Cells Population Growth

Abstract

The optimal control of cancerous cell proliferation is the main contribution of this paper. Chemotherapy is an efficient medical approach to eradicate malignant cells. These drugs are highly toxic and may have lethal side-effects; hence, determining an optimal drug injection protocol has turned into a challengeable problem. To cope with the problem from the system's theory standpoint, a well-known fourth-order nonlinear dynamic model is utilized to describe the system behavior. At first, the solution to the system's differential model is checked by employing the Lipschitz condition. Then, to eradicate tumor cells by minimum drug injection, a nonlinear optimal control technique is proposed. The controller originates the approximate polynomial solution of the Hamilton-Jacobi-Bellman (HJB) nonlinear partial differential equation (PDE). By this method, the complexity of the controller structure can be adjusted by the designer based on the order of the controller. Finally, some simulations are carried out to highlight the effectiveness of the controller in terms of optimality, treatment time, and enlarging of the system's domain of attraction.