Fuzzy Insulin Dosing Policy Design for Type 1 Diabetes Under Different Pump Constraints: An LMI Approach

This paper presents an insulin dosing policy for individuals with Type 1 Diabetes (T1D), utilizing Linear Matrix Inequality (LMI) techniques in combination with the TakagiSugeno (TS) fuzzy approximator. The primary goal is to regulate blood glucose levels by employing robust control strategies for the nonlinear dynamics of the glucose-insulin system, which are described using the Bergman Minimal Model. The proposed approach systematically incorporates insulin pump constraints, such as maximum insulin delivery rates, to ensure practical applicability in real-world scenarios. Simulation results demonstrate that the proposed controller maintains blood glucose levels within a safe range for over 84% of the time, with average glucose levels reduced to as low as 95mg/dL under the least restrictive input constraints. Furthermore, the controller effectively mitigates meal-induced disturbances while minimizing hypoglycemia risks, demonstrating its robustness under varying parameter uncertainties. This research highlights the potential of the proposed method for use in closed-loop insulin delivery systems, offering a promising solution for personalized and adaptive diabetes management.