Nonlinear and Robust Control Strategy Based on Chemotherapy to Minimize the HIV Concentration in Blood Plasma

Abstract

A nonlinear PI-type control strategy is designed in order to minimize the HIV concentration in blood plasma, via medical drug injection, under the framework of bounded uncertain input disturbances. For control design it is considered a simplified mathematical model of the virus infection as a benchmark. The model is based on mass balances of healthy cells, infected cells, and the virus concentrations. The proposed controller contains a nonlinear feedback PI structure of bounded functions of the regulation error. The closed-loop stability of the system is analyzed via Lyapunov technique, in which robustness against system disturbances is demonstrated. Numerical experiments show a satisfactory performance of the proposed methodology as a HIV therapy, in which the virion particles and the infected CD4+T cells are minimized and, as an interesting result, the drug dosage can be suspended, thus avoiding drug resistance from the virus. Finally, the proposed controller is compared to a standard sliding-mode and hyperbolic tangent controllers showing better performance.

Bilinear Robust H∞ Controller to Minimize HIV Concentration in Blood Plasma

“…The mathematical model for the early infection phase of HIV particles and CD4 + T cells originally developed by Tuckwell and Wan [5] and improved by Aguilar-Lopez et al [1]. The model has the nonlinear form as follows…”

“…HIV is a virus that causes Acquired Immune Deficiency Syndrome (AIDS). HIV affects human's immune systems by infecting the CD4 + T cells in blood plasma [1]. CD4 + T cell is a type of lymphocyte which also called by helper T cells.…”

“…Tuckwell and Wan firstly constructed the dynamic system based on the phenomena [5]. Aguilar-Lopez developed the model by adding the control input and disturbance [1]. The constructed model is a nonlinear model which has weakness in the analysis method.…”

Switching control strategy for the HIV dynamic system with some unknown parameters

“…On the other hand, there have been a number of papers investigating the robust control design problems for the HIV model with parameter uncertainties. For instance, a non-linear PI-type robust control was designed in [24] in which a simplified mathematical model of HIV with bounded input disturbances was considered and the HIV viral load was minimised. In [25], the authors proposed a new robust control Lyapunov function (CLF) method for a non-linear uncertain HIV model to reduce the virus count to an undetectable level.…”

“…In [28], a robust feedback controller based on the Root Locus technique and the Routh Hurwitz method was developed to adjust the dosage of reverse transcriptase inhibitors (RTIs) infusion such that the viral load reduction in HIV-infected patients was achieved. Whereas the above papers [24][25][26][27] have some constraints or weaknesses which may be relaxed or improved. For instance, the considered uncertainty and disturbance in [24] were bound by a constant bound even some uncertainties were dependent on states.…”