TUMOR VOLUME GROWTH CONTROL USING BIFURCATION APPROACH

Abstract

A tumor growth system with immune response and chemotherapy is put in a nonlinear dynamical system whose solutions are relative to the initial data. This study presents a phase space analysis of the system. Here, the basin of equilibrium points attraction is determined for a particular class of systems and is subjected to input and state constraints in which all points in phase space would be close to the equilibrium points according to the region of attraction it starts. The addition of a drug term to the system can move the solution trajectory to the desirable basin of attraction. The proposed method gives static output feedback controllers that guarantee the convergence of the generic solutions. Although such a set-point regulation problem is too challenging for general nonlinear systems, the standard surface is found by the proposed approach, which is called separatrix for the controller. This criterion of separating border can perform well even when the mentioned system has limited change parameters. The control is set by separatrix in which the output feedback controller therapy can take all solutions to the healthy state through a constrained chemotherapy protocol. Moreover, this protocol can enable globalization of healthy equilibria.