Uncertainty Characterization and Robust Control of Blood Glucose in Type 1 Diabetic Patients

该项目的目标是开发一个框架，以解释1型糖尿病患者的变异性，并开发一种对这种变异性不敏感的胰岛素给药模式。由于各种原因，开发管理1型糖尿病的解决方案具有挑战性，包括缺乏良好校准的长寿命传感器，不同年龄，性别和体重指数的人如何对胰岛素做出反应的可变性，以及在葡萄糖传感器和胰岛素泵故障存在的情况下确保患者健康的自动胰岛素输送系统的可靠性。一个全面的方法，跨越学科的建模，不确定性量化，预测和控制将允许控制器的设计，保证鲁棒性的病人到病人的变化，导致过渡到动物和人体测试。根据预测，本世纪出生的儿童中有三分之一将患糖尿病，因此，与改善该疾病的治疗相关的保健费用的潜在节省是巨大的。 数学工具将被开发，这将提供一种新的合成控制器的方式来调节1型糖尿病患者的血糖。结果将提供一个统一的框架，表示与随机输入和测量噪声，随后可用于控制器设计的时不变模型的不确定性。多项式的混沌方法来表示时不变的不确定性，再加上映射到伯恩斯坦多项式，允许确定不断变化的状态的界限。 一个概率约束，以迎合随机输入结合不断变化的边界上的状态将允许控制器的设计，这是强大的1型糖尿病患者的变化。

The objective of this project is to develop a framework to account for variability across type 1 diabetes patients and develop an insulin delivery paradigm which is insensitive to such variability. Developing solutions to manage type 1 diabetes are challenging for a variety of reasons including lack of well calibrated long-lived sensors, variability in how people of different ages, sex, and body mass index respond to insulin, and reliability of automated insulin delivery system that ensure the well-being of the patient in the presence of glucose sensor and insulin pump faults. A comprehensive approach spanning the disciplines of modeling, uncertainty quantification, forecasting and control will allow controller designs that promise robustness to patient-to-patient variability, leading to the transition to animal and human testing. With the projection that one in three children born this century will develop diabetes, the potential savings in health care costs associated with improved treatment of the disease is substantial. Mathematical tools will be developed that will provide a new way of synthesizing controllers to regulate blood glucose in type 1 diabetic patients. The results will provide a unified framework for representing time-invariant model uncertainties in conjunction with stochastic inputs and measurement noise which can subsequently be used in controller design. The polynomial chaos approach to representing time-invariant uncertainties, coupled with a mapping to Bernstein polynomials, permits determining bounds on the evolving states. A probabilistic constraint to cater to the stochastic input in conjunction with the evolving bounds on the states will permit controller design which is robust to variations across type 1 diabetes patients.