In this paper, we discuss the first application of recently developed L1-adaptivecontrol methods for the closed-loop control of anesthesia delivery during surgery.Our initial objective, described herein, is to design controllers that are robust tointer-patient variability, such that patients follow a prespecified Bispectral Index(BIS) profile. The controllers are then evaluated on their ability to reject thedisturbances effects on the patients’ BIS trajectory that arise during the courseof surgery. The controllers are designed using identification-based models constructedusing clinical trial data. Two different L1-adaptive control schemes,a state-feedback scheme and an output-feedback scheme, will be evaluated andcompared in terms of tracking performance, amount of anesthesia used, and robustnessto interpatient variability.