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

In this paperý, ýa 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 individualsý. ýThe MOOCPý, ýwhich uses a mathematical model of HIV infectioný, ýhas some incompatible objectivesý. ýThe objectives are maximizing the survival time of patientsý, ýthe level of D4ý ýT-cells and the level of cytotoxic T-lymphocytes (CTLs)ý, ýand minimizing the viral load and the drug costsý. ýIn this approach the fuzzy goals described by the linear membership functionsý, ýare 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)ý. ýUsing the minimum operator for aggregation of fuzzy goalsý, ýthe FGOCP is converted into a constrained optimal control problem (OCP) in canonical formý. ýThe control parametrization enhancing technique (CPET) is used for approximating the OCP by an optimal parameter selection problemý, ýwith the final goal of implementing continuous and interrupted (structured treatment interruptionsý, ýSTI) combinations of reverse transcriptase inhibitor (RTI) and protease inhibitor (PI) drug efficaciesý. ýEfficiency of the proposed method is confirmed by numerical simulations.