It is demonstrated that the reachability paradigm from variable structure control theory is a suitable framework to monitor and predict the progression of the human immunodeficiency virus (HIV) infection following initiation of antiretroviral therapy (ART). A manifold is selected which characterises the infection-free steady-state. A model of HIV infection together with an associated reachability analysis is used to formulate a dynamical condition for the containment of HIV infection on the manifold. This condition is tested using data from two different HIV clinical trials which contain measurements of the CD4+ T cell count and HIV load in the peripheral blood collected from HIV infected individuals for the six month period following initiation of ART. The biological rates of the model are estimated using the multi-point identification method and data points collected in the initial period of the trial. Using the parameter estimates and the numerical solutions of the model, the predictions of the reachability analysis are shown to be consistent with the clinical diagnosis at the conclusion of the trial. The methodology captures the dynamical characteristics of eventual successful, failed and marginal outcomes. The findings evidence that the reachability analysis is an appropriate tool to monitor and develop personalised antiretroviral treatment.