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In this paper, model predictive control (MPC) strategies are applied to the control of human immunodeficiency virus infection, with the final goal of implementing an optimal structured treatment interruptions protocol. The MPC algorithms proposed in this paper use a dynamic model recently developed in order to mimic both transient responses and ultimate behavior, and to describe accordingly the different effect of commonly used drugs in highly active antiretroviral therapy (HAART). Simulation studies show that the proposed methods achieve the goal of reducing the drug consumption (thus minimizing the severe side effects of HAART drugs) while respecting the desired constraints on CD4+ cells and free virions concentration. Such promising results are obtained with realistic assumptions of infrequent (possibly noisy) measurements of a subset of model state variables. Furthermore, the control objectives are achieved even in the presence of mismatch between the dynamics of true patients and that of the MPC model.