Time-optimal control for the induction phase of anesthesia

This paper deals with the control of the induction phase of anesthesia. The objective during this first phase is to bring the patient from its awake state to a final state corresponding to some given depth of anesthesia, measured by the BIS (Bispectral index), within a minimum time. This optimal time control strategy is addressed by means of the maximum principle of Pontryagin. Furthermore, since the anesthesia model presents multiple time scale dynamics that can be split in two groups : fast and slow and since the BIS is a direct function of the fast ones, we only consider the optimal control of fast states. The final state of the slow dynamics is let free. The synthesis approach of the optimal control is detailed then tested in the case of a nominal patient.