Optimized Feedforward Control for the Co-administration of Propofol and Remifentanil for Induction of Hypnosis in General Anesthesia

General anesthesia is a crucial component of invasive medical procedures. Our primary focus is the optimization of the simultaneous infusion of propofol and remifentanil during induction. In particular, we compute a feedforward infusion rate that minimizes the time for bringing the Bispectral Index (BIS) value below an assigned threshold, while ensuring that the BIS remains above an assigned minimum value. We consider a two-drug model, that takes into account the synergistic effect of the two drugs. Due to the expression of the Hill function, the constraint of maintaining the BIS in a given interval is non-convex. We propose a convex tightening to formulate the overall optimal control task as a convex optimization problem. Through simulation experiments, we show that this hybrid feedforward-feedback strategy quickly achieves the BIS target, while maintaining safe and clinically acceptable infusion rates.