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

Abstract

Human Immunodeficiency Virus (HIV) is a type of virus which attacks CD4 + T cells. Insufficient numbers of CD4 + T cells will affect the performance of immunity systems so that someone become riskier to have AIDS or other diseases. HIV phenomenon is modelled as nonlinear system with disturbance, but there is no exact method to solve problems that related with analyzing nonlinear systems with control treatment. Thus, the nonlinear system is approximated into a bilinear system by using Carleman bilinearization method. A robust -controller is designed as a control input to accomodate the disturbances in the dynamic system. Generally, the treatment for HIV is merely to obstruct the replication process. Therefore, the robust control input is described as the chemotherapy of hypothetical drugs which aimed to clear off the HIV concentration in blood plasma. Robust -control is designed with the coefficient matrix of the bilinear system. The simulation result is analyzed by comparing the effect of the robust control toward bilinear and nonlinear system. From numerical simulations, an individual will experience heavy symptom if the hypothetical drugs chemotherapy is not given. This finding is strengthening the urgency of robust control as a chemotherapy with a waiting time. Based on the numerical simulation with robust -control input, bilinear system has trends that give similar interpretation with the trends of nonlinear system. Besides that, robust -control on bilinear system has demolishing speed of HIV concentration and infected CD4 + T cells concentration which approximately equal to the demolishing speed from nonlinear system. Therefore, we can conclude that the performances of -control on bilinear system is nearly same as the performances of nonlinear system.The HIV replication cycle is divided into six stages [2], [4]. The stages are binding and entry, uncoating, reverse transcription, provirus integration, virus protein and assembly, and budding. In each stage of the HIV replication cycle, antiretroviral therapy is given as the efforts to decrease the concentration of HIV particles. Zidovudine (AZT) is the first registered drug which declared effective to fight HIV. The best condition that a person with HIV could have is having a treatment with the combinations of drugs. The combinations must be able to resist at least two out of six stages of the HIV replication.Some mathematical works have been done in modelling this HIV replication in blood plasma. 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. Compared to linear or bilinear systems, nonlinear systems have no specific method to analyze the behavior of the system's state. The state feedback for the nonlinear system has studied in [6]. The other approach, the nonlinear system is approximated by a bilinear system in order to be able to analyze the performance [7...

Cancer Growth Treatment Using Immune Linear Quadratic Regulator Based on Crow Search Optimization Algorithm

“…For instance, reducing the number of cancer cells using successive state dependent algebraic Riccati equation (SDARE) have been introduced in (Arum, Handayani & Saragih, 2019). In (Saputra, Saragih & Handayani, 2019) 𝐻 ∞ were used to control the controller input into a system, the results showed the effectiveness of the 𝐻 ∞ controller in reducing the number of Human Immunodeficiency Virus (HIV) particles in the blood plasma; In (Anelone, Villa-Tamayo & Rivadeneira, 2020) impulsive controller is designed to deliver a personalized dose for each case, and feedback controller showed a tumor reduction potential better than that obtained by former protocols.…”