Robust H ∞ glucose control in diabetes using a physiological model

A robust H ∞ controller was developed to deliver insulin via a mechanical pump in Type I diabetic patients. A fundamental nonlinear diabetic patient model was linearized and then reduced to a third‐order linear form for controller synthesis. Uncertainty in the nonlinear model was characterized by up to ±40% variation in eight physiological parameters. A sensitivity analysis identified the three‐parameter set having the most significant effect on glucose and insulin dynamics over the frequency range of interest ω = [0.002, 0.2] (rad/min). This uncertainty was represented in the frequency domain and incorporated in the controller design. Controller performance was assessed in terms of its ability to track a normoglycemic set point (81.1 mg/dL) in response to a 50 g meal disturbance. In the nominal continuous‐time case, the controller maintained glucose concentrations within ±3.3 mg/dL of set point. A controller tuned to accommodate uncertainty yielded a maximum deviation of 17.6 mg/dL for the worst‐case parameter variation.