Nonlinear Uncertain HIV-1 Model Controller by Using Control Lyapunov Function

Abstract

In this paper, we introduce a new Control Lyapunov Function (CLF) approach for controlling the behavior of nonlinear uncertain HIV-1 models. The uncertainty is in decay parameters and also external control setting. CLF is then applied to different strategies. One such strategy considers input into infected cells population stage and the other considers input into a virus population stage. Furthermore, by adding noise to the HIV-1 model a realistic comparison between control strategies is presented to evaluate the system's dynamics. It has been demonstrated that nonlinear control has effectiveness and robustness, in reducing virus loading to an undetectable level.

Dynamical conditions for the containment of HIV infection by CD8+ T Cells — A variable structure control approach

“…Furthermore, this condition encompasses the nonlinearities of the model and exhibits some robustness properties with respect to parameter and modelling uncertainty. A variety of control techniques have been considered to analyse HIV dynamics in vivo [9], [1], [25], [6]. Evaluating the condition for the containment of HIV infection by the HIV-specific CD8+ T cell response using a Variable Structure Control (VSC) approach is supported by the following observations:1-the dynamics of the CD8+ T cell response has been shown to behave as a switched control system in [3].…”

Modelling the self-tolerance mechanisms of T cells: An adaptive sliding mode control approach

“…The dynamical behaviour of the immune system with respect to changes in one or more parameter values is analysed. A similar survey of variation of biological parameter values has been conducted for studying the robust performance of the controller enhancing the immune response in HIV dynamics [1], [20]. An increase or decrease in the natural decay rates affecting the performance (settling time) of the adaptive control action as in [1].…”

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

“…In order to present the simulation results of the proposed design, we assume there are some uncertainties in the model (25) x˙1…”

“…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.…”