In this paper, a controller is proposed to automate the injection of propofol and remifentanil during general anesthesia using bispectral index (BIS) measurement. To handle the parameter uncertainties due to inter- and intra-patient variability, an extended estimator is used coupled with a Model Predictive Controller (MPC). Two methods are considered for the estimator: the first one is a multiple extended Kalman filter (MEKF), and the second is a moving horizon estimator (MHE). The state and parameter estimations are then used in the MPC to compute the next drug rates. The methods are compared with a PID from the literature. The robustness of the controller is evaluated using Monte-Carlo simulations on a wide population, introducing uncertainties in all parts of the model. Results both on the induction and maintenance phases of anesthesia show the potential interest in using this adaptive method to handle parameter uncertainties.