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The objective of the paper is to develop an open loop insulin infusion profile, which is capable of controlling the blood glucose level of people with Type 1 diabetes in the presence of broad uncertainties such as inter-patient variability and unknown meal quantity. For illustrative purposes, the Bergman model in conjunction with a gut-dynamics model is chosen to represent the human glucose-insulin dynamics. A recently developed sampling based uncertainty quantification approach is used to determine the statistics (mean and variance) of the evolving states in the model. These statistics are utilized to define chance constraints in an optimization framework. The solution obtained shows that under the assumptions made on the distribution of the model parameters, all possible glucose trajectories over time satisfy the desired glycemic control goals. The solution is also validated on the FDA approved Type 1 Diabetes Metabolic Simulator suggesting that the proposed algorithm is highly suitable for human subjects.

Glycemic Control of People With Type 1 Diabetes Based on Probabilistic Constraints