Abstract
This chapter deals with the control of anesthesia taking into account the positivity 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 subsystem 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.
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Notes
- 1.
The time dependence is omitted for simplicity of the notation.
- 2.
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Tarbouriech, S., Queinnec, I., Garcia, G., Mazerolles, M. (2017). Control of Anesthesia Based on Singularly Perturbed Model. In: Cacace, F., Farina, L., Setola, R., Germani, A. (eds) Positive Systems . POSTA 2016. Lecture Notes in Control and Information Sciences, vol 471. Springer, Cham. https://doi.org/10.1007/978-3-319-54211-9_2
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