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.

中文翻译：

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用于使用丙泊酚调节麻醉过程的稳健模型预测控制框架

在这项工作中，我们提出了一种基于线性矩阵不等式 (LMI) 的稳健模型预测控制 (MPC) 策略，用于静脉注射丙泊酚，一种用于手术期间麻醉的药物。控制器是为一群患者设计的，并考虑了对给药量和药物浓度分布的限制。文献中可用的详细分区数学模型根据可用数据进行调整，并提供该过程的未来预测。在应用的上下文中，假设只测量麻醉深度（BIS 指数）——因为这在实践中很常见。通过结合状态观察器实时估计系统状态（器官中的药物量）。派生的控制方案，与设计的状态观察器一起能够应对控制麻醉深度的主要挑战，这些挑战包括患者间和患者内的可变性、模型非线性和模型不确定性。控制器能够满足数据集患者的不同特征，同时满足所有强加的约束。此外，我们表明，通过考虑具有相似特征的较小患者组，相应的反应得到显着改善。