Control of Anesthesia Based on Singularly Perturbed Model

Sophie Tarbouriech (1) , Isabelle Queinnec (1) , Germain Garcia (1) , Michel Mazerolles (2)

1 LAAS-MAC - Équipe Méthodes et Algorithmes en Commande
2 Pôle Anesthésie Réanimation [CHU de Toulouse]

This chapter deals with the control of anesthesia taking into account the pos-itivity together with the upper limitation constraints of the variables and the target interval tolerated for the depth of anesthesia during a surgery. Due to the presence of multiple time scale dynamics in the anesthesia model, the system is re-expressed through a singularly perturbed system allowing to decouple the fast dynamics from the slow ones. Differently from general approaches for singularly perturbed systems , the control objective is then to control and accelerate the fast system without interest in modifying the slow dynamics. Thus, a structured state feedback control is proposed through quasi-LMI (linear matrix inequalities) conditions. The characterization of domains of stability and invariance for the system is provided. Associated convex optimization issues are then discussed. Finally, the theoretical conditions are evaluated on a simulated patient case.

Mots clés: Control of anesthesia; BIS; Positive constraints; Singularly perturbed system; State feedback; LMI Linear Matrix Inequalities

Domaines: Automatique / Robotique

Sophie Tarbouriech, Isabelle Queinnec, Germain Garcia, Michel Mazerolles. Control of Anesthesia Based on Singularly Perturbed Model. Positive Systems - Theory and Applications (POSTA 2016), 471, Springer, pp.17 - 29, 2017, 978-3-319-54210-2. ⟨hal-01573825⟩