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来解释1型糖尿病患者的可变性，并开发一种对这种可变性不敏感的胰岛素给药范例。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，包括缺乏校准良好的长寿命传感器，不同年龄、性别和体重指数的人对胰岛素反应的可变性，以及自动化胰岛素输送系统的可靠性，该系统可确保在存在葡萄糖传感器和胰岛素泵故障的情况下患者的健康。一种跨越建模、不确定性量化、预测和控制学科的综合方法将允许控制器设计，承诺对患者之间的可变性具有稳健性，从而过渡到动物和人类试验。据预测，本世纪出生的儿童中，每三个人中就有一个会患上糖尿病，因此，改进这种疾病的治疗方法，可能会节省大量的医疗费用。将开发数学工具，为合成控制器来调节1型糖尿病患者的血糖提供一种新的方法。所得结果将提供一个统一的框架，结合随机输入和测量噪声来表示时不变模型的不确定性，这些不确定性随后可用于控制器设计。表示时不变不确定性的多项式混沌方法，加上到Bernstein多项式的映射，允许确定演化状态的界限。为了迎合随机输入的概率约束，结合状态的演变界限，将允许控制器设计对1型糖尿病患者的变化具有健壮性。

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.