Optimized robust combined feedforward/feedback control of propofol for induction of hypnosis in general anesthesia

In this paper an optimized robust feedforward/feedback control strategy for anesthesia induction is proposed. Propofol is used to induce hypnosis and the bispectral index scale (BIS) is employed as an indicator of depth of hypnosis. The control action is divided in two parts, a feedforward action, which acts alone in the first phase of anesthesia induction, and a feedback PID action that concludes the induction by smoothly driving the BIS to the target value. The feedforward action is given by an optimized bolus of propofol that is determined by taking into account the uncertainty of the nonlinear pharmacodynamic model for the effect of propofol on BIS. In particular, the bolus is obtained as the solution of a constrained minimum-time control problem in order to minimize the induction time of anesthesia while preventing the undershoot of the BIS level. Thus the patient's safety is ensured by avoiding side-effects due to drug overdosing. The PID controller is then used in order to compensate for the deviation of the BIS from the theoretical behaviour caused by the effect of inter-patient and intra-patient variability.