Robust control of HIV-treatments using a polytopic model

A robust-control-based treatment designed for Human Immunodeficiency Virus (HIV)-infected patients is studied. The dynamics of the immune system´s response to infection is modeled, using a 5th order nonlinear model with separate efficacy coefficients for Protease Inhibitor (PIs) and Reverse Transcriptase Inhibitors (RTIs). Due to errors in parameter estimation and to the existence of unmodelled dynamics, the immune response is represented as an uncertain system: A polytopic system is constructed that incorporates all possible values of the system parameters. Using robust pole location techniques, a control system that stabilizes the polytopic system was designed. Numerical simulation results, including pharmacokinetical response of the organism to anti-retroviral drugs, show that the control law can lead to a long-term stable condition in even extreme cases.