Blood glucose control for type I diabetes mellitus: A robust tracking H∞ problem

Abstract

In this paper, H ∞ control is applied to obtain a robust controller for the automatic insulin delivery rate. The control action permits to prevent the hyperglycaemic 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. For this purpose, the Glucose Tolerance Curve (GTC) of healthy patients is validated as reference model. A nonlinear compartmental model is linearized around a nominal condition, and then reduced for synthesis design. A measure of robust performance is given by accounting parametric uncertainty to the nonlinear model. Two designs were tested to obtain the H ∞ controller: (i) the classic Riccati equation based and (ii) the Linear Matrix Inequalities approach. The performance of the resulting controllers was verified in simulations by using the original nonlinear model. Sensitivity and complementary sensitivity functions show the nominal and robust performance of the linear closed-loop system. The maximum blood glucose tracking error for the nominal and the worst case condition was 15 mg/dL . Thus, the control scheme can successfully regulate the blood glucose level and reproduce the glucose absorption of a healthy subject in a type I diabetic patient.