Payame Noor University (PNU) Control and Optimization in Applied Mathematics 2383-3130 5 2 2020 07 01 An Adaptive Lyapunov-Based Controller for HIV Treatment کنترل‌کننده تطبیقی لیاپانوف برای درمان ‎HIV‎ 1 10 8163 10.30473/coam.2021.56157.1153 EN Sahar Vaseei School of Mathematics and Computer Science, Damghan University‎, ‎Damghan‎, ‎Iran. Mohammad Reza Zarrabi School of Mathematics and Computer Science, Damghan University‎, ‎Damghan‎, ‎Iran. Journal Article 2020 11 12 In view of the tremendous importance of patients’ stability in medical sciences‎, ‎this paper addresses the application of a sliding mode control in medical devices‎. ‎In doing so‎, ‎we consider a nonlinear dynamic system that shows the mathematical model of the human immunodeficiency virus‎. ‎This nonlinear model has three variable states‎: ‎healthy cells‎, ‎infected cells‎, ‎and free viruses‎. ‎The proposed controller displays the effect of medication on preventing the production of the virus and blocking the new infection‎. ‎This controller ensures the stability of this dynamic system provided for HIV in the event of a bounded disturbance‎. ‎The stability and convergence of this process are proved by the Lyapunov theorem‎. ‎Finally‎, ‎a numerical example is given to demonstrate the efficiency of the proposed method. https://mathco.journals.pnu.ac.ir/article_8163_f5cc888379ff690b5bb5229c3a9af331.pdf