Nonlinear and Adaptive Control of a HIV-1 Infection Model

Abstract

This paper presents algorithms for nonlinear and adaptive control of the viral load in a HIV-1 infection model. The model considered is a reduced complexity nonlinear state-space model with two state variables, representing the plasma concentration of un-infected and infected CD4+ T-cells of the human immune system. The viral load is assumed to be proportional to the concentration of infected cells. First, a change of variables that exactly linearizes this system is obtained. For the resulting linear system the manipulated variable is obtained by state feedback. To compensate for uncertainty in the infection parameter of the model an adaptation mechanism based on a Control Lyapunov Function is designed. Since the dependency on parameters is not linear, an approximation is made using a first order Taylor expansion.