2021 Vol.8 No.1 Review Article American Journal of Drug Delivery and Therapeutics Lyapunov based nonlinear controllers for the treatment of HIV/AIDS Khurram Shahzad, Iftikhar Ahmad* , Yasir Islam Institute of National University of Sciences and Technology (NUST), Islamabad, Pakistan Abstract Human Immunodeficiency Virus (HIV) is a form of virus responsible for destroying or weakening the immune system and causes Acquired Immune Deficiency Syndrome (AIDS). Immune system finds it difficult to fight against life threatening infections and diseases after the attack of this virus. Researchers have proposed many control algorithms of drug injection under antiretroviral therapy for the treatment of HIV/AIDS. In this paper, an updated mathematical nonlinear model of HIV/AIDS has been considered and four Lyapunov based nonlinear controllers namely; Synergetic, Generic Backstepping, Integral Backstepping and Lyapunov Redesign controllers have been designed. The main purpose of proposing the controllers is to regulate the amount of drug, so that the cells may track their desired reference value. Antiretroviral drug doses together with antigen- specific cytotoxic T-lymphocytes play an active role to eradicate HIV/AIDS by destroying infected CD4 cells and free virus and increasing maximum number of uninfected CD4 cells to an adequate level. The proposed nonlinear controllers can reduce maximum amount of steady state error and have fast convergence time. Lyapunov based theory has been used for the analysis of system global stability. Proposed controllers have been simulated under MATLAB/Simulink and detailed comparative analysis of these controllers has been given to study their behavior. Keywords: Terms-HIV/AIDS, Drug doses, Synergetic control, In- tegral backstepping, Backstepping, Lyapunov redesign control, Nonlinear control Introduction Human Immunodeficiency Virus (HIV) is a deadly disease that badly affects the T-helper cells or white blood cells in the immune system and is the main cause of Acquired Immune Deficiency Syndrome (AIDS) [1]. Immune system is the defense or protection system of a human body that is made up of proteins, organs, tissues and cells which play a major role for its regulation [2]. After attacking the white blood cells in the immune system, HIV replicates itself, decreases the number of healthy cells below a certain limit and makes the immune system vulnerable to life threatening infections and cancers [1,3]. The virus is mainly caused by blood transfusion, tissue transplant, semen and vaginal breast milk [3,4]. After acute infection and clinical latency, AIDS is the third or worst stage of HIV which occurs if CD4+T lymphocytes or white blood cells fall below 200 cells/mm3 [5]. Even if CD4+T lymphocytes rise above 200 cells/mm3, that person will still be considered to have AIDS which means that there is no cure for this disease, but it can be controlled by eradicating the large number of infected cells through medication using certain automated control techniques [1]. One of the most common type of treatment of HIV/AIDS is antiretroviral therapy in which drug doses are being used to minimize the rapidly growing infected cells. Many control techniques have been applied for the control of this disease, but uninfected or healthy cells are usually being killed at the same time which is the major drawback. Nonlinear controllers are efficient for dealing with uncertain parameters of the system that have been ignored in the linear control techniques and are helpful to obtain fast convergence of states to their desired references and improve the steady state accuracy. Many mathematical models have been considered to analyze the dynamic behavior of HIV/AIDS [6-9]. Optimal control is the most common control technique that has been applied on different models of HIV/AIDS for reduction of viral load in blood plasma. Lyapunov function for the control of HIV and stability analysis of HIV model have also been discussed in the literature. HIV completes its life cycle in different stages and the drugs used to directly attack the virus cells and interrupt the life cycle of virus at different stages are known as anti-retroviral drugs. These drugs are used in a combination of two or three drugs to target the specific stage of HIV virus as each drug has a specific action and belongs to a specific class. Combination of drugs is known as HIV regimen and may contain three drugs from at least two different classes of drugs. The various classes/types of drugs include protease inhibitors, entry inhibitors, fusion inhibitors, integrase inhibitors, pharmacokinetic enhancers, nucleoside reverse transcriptase inhibitors and Non-nucleoside reverse transcriptase inhibitors. The drugs help in stopping the replication cycle of virus, reduces infection of healthy cells from free virus and increase the effectiveness of drugs to suppress the HIV virus below detectable limits. The drugs are used on daily basis to achieve the goal of reducing HIV drug resistance and increase the patients adherence to drugs. Synergetic control is a robust and chattering free technique, which has finite time convergence, ensures global asymptotic stability, is insensitive to internal and external disturbances and parametric uncertainties. It is a linear approximation of sliding mode control technique which has been applied for stabilizing Medium Voltage DC (MVDC) micro-grids. Backstepping is a recursive control method based on Lyapunov stability theory which designs controller for stabilizing each sub-system and step back from each sub system recursively, for finding the external control input. This technique has been applied for MPPT in PV system. The addition of integral action in Generic Backstepping makes it Integral Backstepping controller which