This paper describes strategies toward model-based automation of intravenous anaesthesia employing advanced control techniques. In particular, based on a detailed compartmental mathematical model featuring pharmacokinetic and pharmacodynamics information, two alternative model predictive control strategies are presented: a model predictive control strategy, based on online optimization, the extended predictive self-adaptive control and a multiparametric control strategy based on offline optimization, the multiparametric model predictive control. The multiparametric features to account for the effect of nonlinearity and the impact of estimation are also described. The control strategies are tested on a set of 12 virtually generated patient models for the regulation of the depth of anaesthesia by means of the bispectral index (BIS) using Propofol as the administrated anaesthetic. The simulations show fast response, suitability of dose, and robustness to induce and maintain the desired BIS setpoint.