Automatic administration of medicinal drugs has the potential of delivering benefits over manual practices in terms of reduced costs and improved patient outcomes. Safe and successful substitution of a human operator with a computer algorithm relies, however, on the robustness of the control methodology, the design of which depends, in turn, on available knowledge about the underlying dose-response model. Real-time estimation of a patient's actual response would ensure that the most suitable control algorithm is adopted, but the potentially time-varying nature of model parameters and the limited number of observation signals may cause the estimation problem to be ill-posed, posing a challenge to adaptive control methods. We propose the use of Bayesian inference through a particle filtering approach as a way to overcome these limitations and improve the robustness of automatic drug administration methods. We report on the results of a simulation study modeling the infusion of vasodepressor drug sodium nitroprusside for the control of mean arterial pressure in acute hypertensive patients. The proposed control architecture was able to meet the required performance objectives under challenging operating conditions.