In this work, we present a robust Model Predictive Control (MPC) strategy based on linear matrix inequalities (LMIs) for the intravenous administration of Propofol, a drug which is used for anesthesia during surgeries. The controller is designed for a population of patients and takes into account constraints on the amount of administered drug and on the drug concentration profile. A detailed compartmental mathematical model available in the literature is adjusted to the available data and provides the future predictions of the process. In the context of the application, only the depth of anesthesia (BIS index) is assumed to be measured-as it is common in practice. The state of the system (drug amount in organs) is estimated in real-time by incorporating a state observer.The derived control scheme, along with the designed state observer are able to deal with major challenges in controlling the depth of anesthesia which are inter-and intra-patient variability, model nonlinearity, and model uncertainty.The controller is able to satisfy the divergent characteristics of the patients of the dataset, while satisfying in parallel all the imposed constraints. Moreover, we show that by considering smaller groups of patients with similar characteristics the corresponding responses are significantly improved.

In this paper an offset-free model predictive control scheme is presented for fractionalorder systems using the Grünwald-Letnikov derivative. The infinite-history fractionalorder system is approximated by a finite-dimensional state-space system and the modeling error is cast as a bounded disturbance term. Using a state observer, it is shown that the unknown disturbance at steady state can be reconstructed and modeling errors and other persistent disturbances can be attenuated. The effectiveness of the proposed controller-observer ensemble is demonstrated in the optimal administration of an anti-arrhythmic medicine with fractional-order pharmacokinetics.

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