Nonlinear Controller Synthesis for HIV Dynamics Based on SOS

Abstract

Nowadays antiretroviral therapy is widely used to cut down the viral burden and cut off a few infection sources in clinical medicine for Human Immunodeficiency Virus (HIV) infected patients, and a lot of evidence have shown that a massive coverage with antiretroviral therapy has already acquired a series of contributions and successes to save life and popularize preventive knowledge. Based on the HIV dynamic model, this paper designs a feedback controller to adjust the concentration values of CD4+T cell, CD8+T cell and viral load in HIV dynamic model to a healthy condition asymptotically. The HIV dynamic model is expressed in the form of a polynomial system and then the control law, as the appropriate drug dosage usually applied in the medical therapy, is designed to suppress the reproduction of the HIV virus and improve the production rate of healthy cell in vivo, simultaneously. According to the polynomial Lyapunov theory and sum of squares (SOS) technique, the conditions for the controller synthesis are proposed. The simulation experimental results can be testified the availability of the proposed method.

Keywords

• Human immunodeficiency virus
• antiretroviral therapy
• polynomial Lyapunov theory
• sum of squares