The Control Parametrization Enhancing Technique for Multi-Objective Optimal Control of HIV Dynamic

Abstract

In this paper‎, ‎a computational approach is adopted for solving a multi-objective optimal control problem (MOOCP) formulation of optimal drug scheduling in human immunodeficiency (HIV) virus infected by individuals‎. ‎The MOOCP‎, ‎which uses a mathematical model of HIV infection‎, ‎has some incompatible objectives‎. ‎The objectives are maximizing the survival time of patients‎, ‎the level of D4‎+ ‎T-cells and the level of cytotoxic T-lymphocytes (CTLs)‎, ‎and minimizing the viral load and the drug costs‎. ‎In this approach the fuzzy goals described by the linear membership functions‎, ‎are incorporated for the objectives and the optimal solution is investigated by maximizing the degree of attainment of the aggregated fuzzy goals resulting a fuzzy goal optimal control problem (FGOCP)‎. ‎Using the minimum operator for aggregation of fuzzy goals‎, ‎the FGOCP is converted into a constrained optimal control problem (OCP) in canonical form‎. ‎The control parametrization enhancing technique (CPET) is used for approximating the OCP by an optimal parameter selection problem‎, ‎with the final goal of implementing continuous and interrupted (structured treatment interruptions‎, ‎STI) combinations of reverse transcriptase inhibitor (RTI) and protease inhibitor (PI) drug efficacies‎. ‎Efficiency of the proposed method is confirmed by numerical simulations.