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.
