A switched control strategy combining minimum time control and dynamic output feedback can theoretically maintain depth of hypnosis during anesthesia.
Switched BIS control may aid hypnosis management; hypothesis-generating and requires randomized validation before practice.
Mimicking the medical practice, this study deals with the control of hypnosis during a surgical intervention thanks to a switched control strategy. The key idea consists in starting with an initial minimum time control for the induction phase followed by a dynamic output feedback for the maintenance phase. The objective during the first phase is to bring the patient from its awake state to a final state corresponding to some given depth of hypnosis, measured by the BIS (Bispectral index), within a minimum time. Then, once the patient state is close to the desired target, the control is switched to a dynamic output feedback ensuring that the BIS stays in a given interval taking into account the saturation of the actuator and the multi‐time scale dynamics in the anaesthesia model. The positivity of the system is also preserved thanks to the use of input saturation and state constraints. The stability of the switched control strategy is addressed and the theoretical conditions are evaluated on different case studies.
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Queinnec et al. (2018) studied this question.
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