A Robust Approach to Control Blood Glucose Level: Diabetes Mellitus Type I

Abstract

H∞ control is applied for the insulin delivery to prevent the hyperglycemic levels in a Type I diabetic patient. From a control theory point of view, the blood glucose regulation problem is reformulated as a tracking one. A glucose tolerance curve (GTC), validated from healthy subjects, is used as reference signal. A nonlinear compartmental model is linearized around a nominal condition, and reduced for the controller synthesis. Two designs were carried out to obtain the H∞ control: i) the classic Riccati equation based and ii) the Linear Matrix Inequalities approach. The performance of the controllers was studied by implementing them into the nonlinear model. Sensitivity and complementary sensitivity functions showthe nominaland robust performance of the closed-loop system. Numericalsimulations sho wthat the maximumblood glucose tracking error is around 15 mg/dL.