This paper proposes an individualized approach to closed-loop control of depth of hypnosis during propofol anesthesia. The novelty of the paper lies in the individualization of the controller at the end of the induction phase of anesthesia, based on a patient model identified from the dose-response relationship during induction of anesthesia. The proposed approach is shown to be superior to administration of propofol based on population-based infusion schemes tailored to individual patients. This approach has the potential to outperform fully adaptive approaches in regards to controller robustness against measurement variability due to surgical stimulation. To streamline controller synthesis, two output filters were introduced (inverting the Hill dose-response model and the linear time-invariant sensor model), which yield a close-to-linear representation of the system dynamics when used with a compartmental patient model. These filters are especially useful during the induction phase of anesthesia in which a nonlinear dose-response relationship complicates the design of an appropriate controller. The proposed approach was evaluated in simulation on pharmacokinetic and pharmacodynamic models of 44 patients identified from real clinical data. A model of the NeuroSense, a hypnotic depth monitor based on wavelet analysis of EEG, was also included. This monitor is similar to the well-known BIS, but has linear time-invariant dynamics and does not introduce a delay. The proposed scheme was compared with a population-based controller, i.e. a controller only utilizing models based on demographic covariates for its tuning. On average, the proposed approach offered 25 % improvement in disturbance attenuation, measured as the integrated absolute error following a step disturbance. The corresponding standard deviation from the reference was also decreased by 25 %. Results are discussed and possible directions of future work are proposed.